Physics Notes For Tenth Class by Muhammad Arif Rattar

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= CHAPTER NO 1 INTRODUCTION OF PHYSICS

Topics of the Chapter a) Introduction of physicsb) Classification of sciencec) Branches of physicsd) Most famous Muslim scientists INTRODUCTION OF PHYSICS: Definition: "It is branch of science which deals that the study about energy and matter interaction between them is called Physics." Energy: Ability of doing work or capacity of doing work is called energy.Matter: Any thing which occupies space and mass is called matter.Classification of Science:

Matter: Any thing which occupies space place and carry mass is called matter. STATE OF MATTER(1) Gas: It has no shape and has no volume. (2) Liquid: It has no shape and has volume. (3) Solid: It has shape and has volume.(4) Plasma: It is a mixture of gas, solid and liquid is called Plasma.

BRANCHES OF PHYSICS

1. Mechanics: It is branch of Physics in which, we study about the motion of particles or bodies is known as Mechanics.

Composed by M Arif Rattar

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= 2. Electricity: It is branch of Physics in which we study about the

involving electric charges and effected is called Electricity, the charges are rest motion.

3. Electromagnetism: It is branch of Physics in which we study about the electricity which produced by magnetic field.

4. Solid-State Physics: It is branch of Physics in which we study about the property of crystalline material only, that is of material constituent in atoms are arranged in three dimensional.

5. Nuclear Physics: It is branch of Physics in which we study about the structural properties and reaction between the nuclei atom.

6. Atomic Physics: It is branch of Physics in which we study about the structure and properties of atoms, theses atom are present in the nucleus.

7. Plasma Physics: It is branch of Physics in which we study about the properties of highly ionized atom forming a mixture of bare nuclei and electrons.

8. Bio Physics: It is branch of Physics in which we study about the application of physical methods and types of explanation to biophysical system.

9. Astro-Physics: It is branch of Physics in which we study about the properties and structure of stars and planets. It is also called Astronomy.

MOST FAMOUS MUSLIM SCIENTISTS

ABU-ALI HUSSAIN IBN-AL-HAITHAM: He was born in 965 A.D... He was born at Basra a historical city of Iraq. He was great scholar of Physics, Mathematics, engineering astronomy and medicine. He worked on optics. It is branch of Physics. His famous book was "Kitab-ul-manazir". He wrote the most wonderful chapter of this book is on human eyes. According to this book "the light on entering the eye makes it emit light rays, which on hitting an object make the object visible to the eye". Some of the incident light rays are reflected from the object and enter the eye. He constructed a pinhole camera and he managed to obtain an image of a "sun eclipse" with its help. He was first scientist to give two laws of reflection of light to the world. He was died in 1039 A.D… AL-BERUNI: The most famous scholar of the golden age of Islam Al-Beruni was born in a small town "Berun" in present day Afghanistan 973 A.D… He wrote a many book under the age of seventy five years. Such are subject as Mathematics Cosmology, Physics Geography, History,


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Culture, Civilization, Archaeology, Comparative Religions, Geology, Chemistry and Biology. Al-Beruni discussed the measurement of earth, the shape of earth, the movement of sun and moon. The phase of the moon and the movement of the moon were known "Planets". Planets about writing the book are "Qanoon-Al-masoodi". He gave the method of determing the longitude and latitude of a place. He also determined the densities of metals. He measured the circumference of the earth. YAQUB KINDHI: The famous Arab Philosopher Yaqub Kindhi was born 900 A.D. in Basra. He produced extensive research monographs on meteorology, specific gravity and especially work is reflection of light. He discussed about musical instruments. He discovered a method express the notes of music in term of frequencies. In addition to sound he also worked on geometrical optics. One his work optic was translated in Latin. MUHAMMAD BIN MUSA KHWARZIMI: He was born in 780 A.D. in the city of Khwarzimi. He was member of institution of learning the "Bait-ul-Haikmat". The two monographs Hisab and Aljabar-wal-Maqabla. He introduced the method of counting based on numbering and decimal system. One important feature of Khwarzimi is algebra is that he is used in geometrical construction for the first time for solving various algebraic problems. He was died in 850 A.D. in the age of 70 years.

NASUR- UD-DIN- MUHAMMAD BIN HASSAN TUSI: The famous Muslim philosopher, Mathematician and scientist Nasir-ud-Din Muhammad Hassan Tusi was born in the city of Iran in 1201 A.D… He was the minister of Halaku Khan. DR: ABDUL QADEER KHAN: He was born on 1st April 1936 A.D. at Bhopal in India. He obtained M.Sc technology degree from Holland. He was selected as research Assistant in the same university. His PhD degree was from leaven Belgium. He worked expert at Urenco enrichment plant in Holland. After returned to Pakistan, the former engineering research laboratories have been named as "A. Qadeer laboratories". He awarded from "Hilal-i-Imatiaz" by the Govt: of Pakistan.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= DR: ABDUS SALAAM: He was born in Jhang a district in the Punjab (Pakistan) in 1926 A.D… His college education from Govt: college Lahore". He passed every examination with distinction. His better results, he was awarded Govt: scholarship for advanced studies in U.K. He came back to Pakistan in 1950 A.D… He was awarded noble prize in Physics in 1979 A.D… For his work is in "Grand Unification Theory"(GUT). They are engaged in their own countries by joining with "Elites of Physics".


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= CHAPTER 2 MEASUREMENT Topics of the chapter:

(a) Introduction of Measurement(b) Fundamental Physical Quantities (c) Fundamental Units(d) Derived Physical Quantities(e) Derived Units(f) Systems of Measurement(g) International System of Units of Measurement(h) Measuring Instruments(i) Problems of chapter

INTRODUCTION OF MEASUREMENT: It is the study of any body or any things measure in the physical quantities is called Measurement.

Fundamental Physical Quantities: These quantities which have used to express or measure the measure the earth or surface of any thing and measure the period at observation or experiment is performed is called Fundamental Physics Quantities.

Fundamental Physical Units: The units used to express or measure in fundamental physical quantities are called Fundamental Physical Quantities. There are three Fundamental Physical Units. They are:

(1)Mass(2)Length (3)Time

Derived Physical Quantities: These quantities which have derived from fundamental physical quantities are called Derived Physical quantities.

Derived Physical Units: The units used to express or measure in Derived physical quantities are called Derived Units.

SYSTEM OF MEASUREMENT: There are three systems of measurement. They are:

(1)C.G.S(2)F.P.S(3)M.K.S


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= CGS System: Centimeter, Gram and Second are fundamental physical units of length, mass and time. In CGS system, the derived unit of force is Dyne. 1Dyne= 1g×1cm/sec:

F.P.S System: Foot, Pound and Second are fundamental physical units of length, force and time. It is British Engineering System. In FPS system the derived unit of mass is slug.1slug= 1P×1F/sec

MKS System: Meter, Kilogram and Second are fundamental physical units of length, mass and time. In MKS system the derived units is force.1Force=1kg × 1m/sec2.

International System of Measurement: It is introduced in 1960 A.D. in the conference of International System of Measuring of weigh, time and length in Paris. It is also called S.I Units of measurement. In this MKS system is upgraded and made S.I system. The fundamental or Basic units length (L), mass (M), time (t), electric current (I) temperature (T), luminous intensity (I υ) and amount of substance (n) are meter (m), kilogram (kg), second (sec), ampere (A), Kelvin (K), candela (cd) and mole (mol). These quantities are listed in table with the symbols Table SI Base/Fundamental UnitsNo. Physical Quantity Name Symbol

01 Time Second s

02 Length Metre m03 Mass Kilogram kg04 Amount of substance Mole mol05 Thermodynamic

temperature Kelvin K

06 Electric current Ampere A 07 Luminous intensity Candela cd The Derived Units:These derived units are obtained from the fundamental units.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= For example: volume of box is equal to length × height that is meter × meter = m2

Meter is fundamental quantity; so meter cube is derived units. Similarly speed, acceleration, force, density, area etc are derived quantities and their units are derived unitsThe Derived unit speed (v), acceleration (a), volume (V), force (F), pressure (P), work (W) and charge (Q) are meter/second (), meter second2

(m/sec2), meter cubic (m3), Newton (m.kg/sec2), Pascal a (N/m2), Joule j (Nm), coulomb C (A.s) Some derived quantities and their derived units with their symbols are given below:

These quantities are given in the table on next page.

TABLE SI DERIVED UNITSS.no Derived Quantity Symbol Unit Unit symbol01 Speed v Meter/second m/sec 02 Acceleration a Meter/second2 m/sec2

Volume V Cubic meter m3

04 Force F Newton N(m.kg/sec2)05 Pressure P Pascal Pa(N/m2)06 Work W Joule J(N.m)07 Charge Q Coulomb C(As)

Smaller and bigger units or prefixes units

Bigger Units Smaller UnitsDeca- D - 101 Pico – P- 10-12

Hecto – H – 102 Nano – n – 10-9

Kilo – k – 103 Micro – µ – 10-6

Mega – M – 106 Milli – m – 10-3

Giga – G – 109 Centi – c - 10-2

Tera – T- 1012 Deci – d – 10-1

Example: 2.1 Data L= 2.52 cm (i) mm = (ii) m = ?


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= We know that,

(i) 1cm = 10 mm 2.52 cm = 2.52 × 10 = 25.2mm Ans

(ii) 1cm = 0.01 m 2.52 cm = 2.52 × 0.01 = 0.0252 m Ans

Example: 2.2 Data

Wave length = 7000 × 10-10 m (i) µm =? (ii) mm = ? We know that,(i) 1 m = 106 µm = 7000 × 10-10 × 106 µm = 7000 × 10-4 µm Ans

(ii) 1 m = 103 mm = 7000 × 10-10 × 103mm = 7000 × 10-7 mm Ans

Example: 2.3

Data Mass = 3.635 g

(j) µg =?(ii) mg = ?

(iii) kg = ?We know that,

(i) 1 g = 106 µg 3.635 g = 3.635 × 106 µg = 36350000 µg Ans

(ii) 1 g = 103 mg 3.635 g = 3.635 × 103 mg = 36350 mg Ans

(ii) 1 g = 10-3 kg 3.635 g = 3.635 × 10-3 mg


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar =============================================================

= 0.03635 kg Ans

MEASURING INSTRUMENT: Those instrument or apparatus that used for measurement, physical quantity and duration of event time is called measuring instrument.

VERNIER CALLIPERSAn ordinary meter rod can measure a distance upto 7mm. to measure distances smaller than this the instruments are used. It is used to measure a distance accurately up to 0.1mm. A vernier calliper consists of rectangular steel bar whose one side is graduated in cms. It is known as "main scale". A small scale consisting of 10 division which slides over the main scale is known as "vernier scale."

VERNIER CONSTANT OR LEAST COUNT (LC)Vernier constant or least count is the minimum distance that can be measured with the help of vernier calliper. It is the difference between the value of one main scale and one vernier division. 10 vernier division = 9 main scale = 9 mm 1 vernier division = 9mm 10 = 0.9 mm Least Count = difference between main scale and vernier division. = 1 mm – 0.9 mm = 0.1 mm or 0.01 cmFormula of Least Count: LC = Value of smaller division Total no: of division of VS = 1 mm 10 = 0.01 mm

MICROMETER-SCREW-GAUGEThe vernier callipers can measure up to 1/100 of a cm. It consists of a solid U- shaped frame F of metal. It has a fixed studat with plane roundend and other end B. B passes a fine and accurately cut screw S having a plane roundend. A cap fit on the screw-division 50. Scale graduated in millimeter on the nut of screw. Parallel to the axis of the screw and is called "Linear main scale".

PITCH OF SCREW


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= It is the distance of b/w the two consecutive thread of the linear screw. It is measured by the distance travelled by the circular scale on main scale. During one complete solution of the circular scale.Formula: Least count = Pitch of screw No: of division on the Circular scale L C = 1 / 2 mm = 1 = 1 mm 50 2×50 100 = 0.01 mm or 0.001cm

PHYSICAL BALANCEIt is common device that used for to find the mass of object. It consists of a horizontal beam resting at its middle point on a central knife edge. Two similar pans are suspended on two more knife edges near each end of the beam. A long pointer capable of swinging on a scale PS attached to the middle of the beam the physical balance is leveled on a table by means of leveling screw. The beam is set free by rotating the knobat the front of the balance. The pointer moves towards the side smaller mass by means of two adjustment screw. Standard mass in the pan is adjusted to find the mass of the object.

STOP WATCHIf we are interested to measure time intervals for event we use a special watch known as "Stop Watch". Scales of minutes and seconds hand in it are on a circular dial. Stop watch is set at zero. Pressing and releasing the Knob. The Knob B is pressed and released again the watch start. The second hand complete one rotation of sixty seconds, the minute. Hand advance by division.

MEASURING CYLINDERIt is a glass cylinder with a scale in cubic centimeter or milli- (ml) marked on it. It is used to find the volume liquid. When a liquid is poured, it raises certain height in the cylinder. The level of liquid in the cylinder is noted and the volume of liquid obtained. The cylinder lies on horizontal table.



MEASUTMENT-OF-AREA

It object is regular shape their area. The area of a rectangular object is determined by finding its length and breath.

The area of circular shaped object can be calculated by measuring its radius and then applying formula. π = r2

.: π = 3.14 or 22 7The area is expressed in sq: meter.


25 ml 20 ml 10 ml 05 ml


MEASUREMENT OF VOLUME

h Y-axis→

Z-axis→ W L ↑ x- axis V = height × length × width Volume is the space occupied by an object. Solid has a regular shape. The volume of a rectangular block is founded by measuring its length, breath or width and height.

Volume of block =(length × breath × height) or (l × b × h). The volume of a sphere of radius r is equal to 4/3 π r2

Cross section π r2

Radius The S.I unit of volume is cubic meter (m3). Volume o f liquid is expressed in litres. 1 liltre = 1000 cm3 1 liltre = 1000 mlCHAPTER 3 SCALARS AND VECTORSTopics of the chapter:a) Introduction of Scalar and Vectorb) Representation of a Vector c) Negative of a vectord) Addition of vectors by Head to Tail rulese) Subtraction of vectors

f) Trigonometryg) Resolution of vectorh) Addition of rectangular component of vectors

SCALAR:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Those physical quantities which have only magnitude but no direction are called Scalar, only numbering or suitable units are called scalar quantity. Example: speed, volume, mass, time, work, density, length, temperature, distance.

VECTORS: Those physical quantities which have magnitude and direction for their complete description is called vector, these directional quantities are called vector quantity. Example: Displacement, Velocity, Force, acceleration, momentum etc It is denoted by "arrow (→)" and arrow shows vector quantity.We write as give an arrow upto the capital letter as given below: A has vector and magnitude A Only magnitudeREPRESENTATION OF A VECTOR: Graphically, a vector quantity denoted by direction of a vector. North

West East

South The length of the arrow on certain scale represents the magnitude of

the vector and arrow gives the direction of vector. Tail

5 cm

Head A The velocity of 500 km/h due east is represented by the direction line

OA

Scale = 1 cm = 100 Km/h = 5 cm = 500 km/h Three types of vector of directionX-axis directionY-axis direction A Z-axis direction y-axis F


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= 30° θ x-axis

z-axis

Required the vectors1. x-axis direction 2. y-axis direction3. Force of direction 4. Angle

NEGATIVE OF A VECTOR: A

-A

These vectors which have same magnitude but its direction is opposite to that of vector A is called "Negative vector".ADDITION OF VECTOR: The adding of vectors two or more than two but they have different in direction is called Addition of vector.ADDITION OF VECTOR BY HEAD TO TAIL RULE METHOD: The sum of vectors is different from that of scalar addition. While adding vectors we have to take cover direction, In addition to

magnitude. The sum or resultant vector of two or more vectors is a single effects

as the combine effects of all the vectors. B

A

R B

A


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= R = A + B if we have two vectors A to B their resultant vector is R .SUBTRACTION OF VECTORS: In the order to subtract a vector from another vector the sign o f the vector to be subtracted is changed and then adds to their vector.For Example: If vector B is subtracted from vector A. A – B A – B = A + (- B) A – B = A – B

A B - B

A - B

A – B AB = AB + BC AB = A + (- B) AB = A – B TRIGONOMETRY: It is important branch of mathematics, and it is used to solve various problems in physics it we denoted angle of vectors and direction. It introduced by Muhammad Bin Musa Khwarzmi Tri + gono + metry = three + angle + measurement. B Hypotenuse perpendicular

θ Triangle O A Base


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= The ratio between two sides of the right angled triangle is represented by different names 1. Sine θ2. Cosine θ3. Tangent θ

Sin θ = AB = Perpendicular OA Base

Cosine θ = OB = Base OA Hyp: Tangent θ = AB = Perpendicular OB Base

TABLE OF TRIGONOMETRIC RATIO

RESOLUTION OF VECTORS: A vector has into its components. The process of slitting a vector into its parts is called resolution of vector. These parts may acting different directions and are called "the components of that vector." We can resolve a vector into a number of components, but generally a vector is resolved into two components at right angle to each there are called "rectangular components." The component along horizontal direction is called "Horizontal component of the vector". The component along vertical direction is called "Vertical components of the vector".

B y-axis F Fy

Fx O x-axis


S.no Angle Sin θ Cos θ Tan θ

01 0° 0 1 0

02 30° 0.5 0.866 0.577

03 45° 0.707 0.707 1

04 60° 0.866 0.5 1.73

05 90° 1 0 0

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= A

.: Fx, FyThere are two rectangular components. Such Fx, Fy of vector F .: Fx = OA = Base = Cos θ OB Hyp: → (1)

It is a horizontal component. .: Fy = AB = perpendicular = Sin θ OB Hypotenuse → (2)It is vertical components.ADDITION OF RECTANGULAR COMPONENT OF VECTORS: We have two perpendicular vectors AB and BC, denoted by Fx and Fy. C F Fy A B FxAC = AB + BCF = Fx + Fy As, ABC is a right angled triangle AC = √ (AB)2 +(BC)2 F = √(Fx)2 + (Fy)2

Resolve the direction and angle Tan θ = Fy Fx


Fx = F Cos θ

Fy = F Sin θ

θ = tan-1 Fy Fx


CHAPTER NO 4 KINEMATICS

Topics of the chapter:a) Kinematics b) Rest c) Motion and its types d) Distance, Speed and its types e) Displacement, Velocity and its typesf) Acceleration and its typesg) Deceleration h) Three equation in Kinematics 1. vf = vi +at 2. s = vit +1/2 at2 3. 2as = vf 2 – vi 2 i) Motion under gravity (Free fall motion)

KINEMATICS: It is the branch of the mechanics which deals with the study of motion of objects without reference to the force or agent is called "Kinematics" For Example: Motion of car, walking of man and motion of ball etc.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= REST: A body does not change its position but remain same place. OR If a body does not change their place from A point to B point is called "Rest".MOTION: A body changes its position but not remain same place. OR If a body changes its position from A point to B point OR An object change their position from one place to another place is called "Motion" TYPES OF MOTION: There are three types of motion. They are:1. Translatory Motion2. Rotation Motion 3. Oscillatory (Vibratory) MotionTRANSLATORY MOTION: A motion of a body in which every particles of the body is being displaced by the same amount is called Translatory motion. OR An object moves a straight path.

A B EXPLANATION: A car is moving a straight path A to path B but this path is straight pathROTATION MOTION: When an object spins or rotates about a fixed point or axis its motion is called rotational motion. Example :(1) Earth rotates in own axis. (2) An electron rotates in orbit around the nucleus.

OSCILLATORY (VIBRATORY) MOTION: Such a motion to fro motion of an object about mean position is called Oscillatory motion. OR A motion is here and there motion is called Oscillatory motion.



Sample Pendulum

EXPLANATION: When a pendulum swings from one side to other side and back the motion of pendulum is to and fro motion. The motion of pendulum is example DISTANCE, SPEED AND ITS TYPES: Distance: Two points or line which has magnitude but no direction is called Distance. A B 100 m It has scalar quantity and it is denoted by "s"Speed and its types: Total distance covered per unit time is called Distance. OR The ratio of total distance covered by total time is called Distance 100 m A B 60 sec It has scalar quantity Equation: Speed (v) = total distance covered (s) Total time (t) v = s_ tIts SI unit is m/s(1) Average speed: Total distance covered in average by interval time is called average speed.

Vav = s_ t DISPLACEMENT, VELOCITY AND ITS TYPES:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Displacement: The two points have direction and as well as magnitude is called Displacement. OR Shortest distance between two points is called Displacement. North A West East

B South Velocity and its types: Velocity: Total displacement covered per unit time is called Velocity. OR The time rate change of displacement is called Velocity.It is a vector quantity and it denotes by "V"Mathematically we can be written by V = S_ T That means the speed of the body in different direction is its called velocity.It is a vector quantity and its S.I unit is m/sAverage Velocity: Total displacement is covered in interval time is called average velocity. Vav = Total displacement covered Total time OR

Vav = S_ T Acceleration and its types: Acceleration: The rate of velocity is called Acceleration. OR if a body is moving a velocity with respect to time is called accelerationExplanation: If the speed is increasing then acceleration is positive. If the speed is decreasing then acceleration is negative or retardation. The


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= positive acceleration is same direction. The negative acceleration is opposite direction.Acceleration is a vector quantity. Velocity (+ve) Velocity (+ve) + ve – ve Negative Acceleration

Mathematically formula

a = ∆V ∆ ta = V a = Vf – Vi t t.: ∆V = Vf – Vi There are two factors in acceleration.1. Initial Velocity (Vi)2. Final Velocity (Vf) The unit of acceleration in S.I system m/s2 or ms – 2

Uniform Acceleration: If a velocity body is moving a along a straight line changes uniformly in equal time. OR If a body moving with uniform velocity is called uniform acceleration.Average Acceleration: The ratio between total change in velocity and time is called average acceleration .: a av = ∆V ∆ tDeceleration or Retardation: If a car is moving with its acceleration , when driver apply the bricks the deceleration or retardation is produced.Equation in Kinematics:There are three equations in Kinematics.

1. Vf = Vi + at 2. s = Vit + 1/2 at2

3. 2as = Vf 2 – Vi 2

First equation: If an object is moving with uniform acceleration and its velocity change initial velocity (Vi) to final velocity (Vf) in time interval t


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Vf = Vi + at Solution Vf = Vi + at .: a = Vi – Vf t a = Vi –Vf t by cross multiplication at = Vi – Vf Change the side of Vi at + Vi = -Vf Now the change side of Vf Vf = at +Vi And now rearrangement of at + Vi Vf = Vi + at Hence proved

Second Equation: A body starts with an initial velocity Vi and moves for t second with a acceleration so that final velocity become Vf. We find the distance S = Vit +1/2 at 2

Solution S = vt .: V = Vi +Vf 2S = Vi + Vf × t 2 S = Vi + Vi + at ×t .: Vf = Vi+ at 2S = 2 Vi + at ×t 2 2

S = Vit + 1 at 2

2

Hence proved

Third Equation: It is related to motion. Initial velocity, the final velocity, acceleration and distance traveled 2as = Vi 2 + Vf 2

Solution


S = Vit + 1 at2

2

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= S = Vt .: V = Vf +Vi & t = Vf – Vi 2 a S = Vf + Vi Vf – Vi 2 a

S = Vf 2 - Vi 2 2a By cross multiplication 2as = Vf 2 – Vi 2

2as = Vf 2 – Vi 2 Hence Proved

Motion under Gravity (Free fall motion): If we drop a body from certain height. It falls to the ground with a velocity continues to increases till it. It was introduced by the Galileo an Italian scientist dropped several bodies from tower in Pisa. Acceleration is freely falling body is called acceleration is due to gravity and denoted by "g". Its value is 9.8 m/s 2 These three equations will be applied in the free fall motion.

1. Vf = Vi + gt2. s = Vit +1/2 gt 2

3. 2gs = Vf 2 – Vi 2

CHAPTER NO 5 FORCE AND MOTIONTopics of the chapter:(a)Force (b)Newton's Laws of Motion(c) Mass and Weight (d)Momentum and Law of conservation of momentum(e) Friction(f) Rolling Friction

FORCE: It is an agent which the changes or tends to change the state of rest the motion of a body is called Force. Its S.I unit is Newton or N.Unit of Force:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= The unit of force is Newton (N= kg.m/s 2). It is denoted by N. It can be defined as fellows: "A force which produces an acceleration of one metre per second on a mass of one kilogram is known as one Newton"Newton's Laws of Motion: There are three laws of motion. Now we discuss about these laws of Newton.Newton's First Law of Motion: This law states that "Every object continues its state of rest or uniform motion in a straight line, unless it is act upon by an external force" ORIf the total force of object is zero, its centre of mass continues is in the same of the motion.Example: A book lying on the table will remain their for ever in the same position unless some one comes and removes it position. Conclusions: 1. Force is an agent which produces or tends to produce a change in the

state of rest of motion. 2. All material object posses the property of opposing any change in their

state of rest or uniform motion. This property is known as "Inertia" Inertia is the tendency of an object to resist a change in its state is called "Inertia".

Therefore the first law of motion is also called the law of inertia. Newton's Second law of Motion:This law state that "When force is applied on a object, it will be produce acceleration in its own direction." Force is directly proportional to the magnitude of force and inversely proportion to the mass of the object. F F a a

Different force acting on the same mass F F a a Mathematically we can be writtenAcceleration is directly proportional to the Force and mass is constant. a ∝ F(Mass is constant) → (1)Mass is inversely proportional to the acceleration and force is constant. a ∝ 1/ m (Force is constant) → (2)Combine both equation (1) and (2)


A A

A B

Same force acting on the different masses

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= a ∝ F/mNow remove the sign of the proportionality and use constant K. a = K F/m The value of K is 1. Therefore a = 1. F/m OR F = ma The unit of force is the Newton (N= kg/m 2).Newton's Third law of Motion: This law state that "Every action there is equal and opposite in the reaction." OR action or reaction of forces but opposition in the direction of motion. Both reaction and reaction between the forces.For Example: Let a person throws a ball on a wall. The ball bounces back is due to the reason that the ball exerts a certain force on the wall. This is called action of the ball on the wall. In response the wall also exerts a force of the same magnitude on the ball which is called reaction of the wall on the ball, and hence the ball bounces back. F

F

Mass and Weight:Mass: .: m = F/aThe ratio between force and acceleration is called mass. It has inertia. Mass has no direction so it is scalar quantity. Mass of body is remain constant.The S.I unit of mass is kilogram and this can be measured in laboratory by an ordinary balance. Weight: F = ma a = g (g = gravity) W = mg The force by which is the earth attracts to the body toward centre. The mass body is m and its acceleration is due to gravity. Weight of body is not remain same. Direction is always toward centre of earth.


Reaction of the wall

Action of the ball

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= It is due to this attraction that the bodies which are not too far from earth's surface, fall with the same acceleration. This acceleration is called the acceleration due to gravity and is denoted by g. since weight is force therefore the second law of motion (F = ma) DIFFERENT BETWEEN MASS AND WEIGHT:

MOMENTUM AND LAW OF CONSERVATION OF MOMENTUM:

Momentum: Momentum is defined as the "product of mass and velocity of object and its denoted by P". The property of moving object is called momentum. The S.I unit of momentum is kg.m/s and it is vector quantity. Momentum is the direction of velocity. P = m. vFor example: A bullet has a mass of 10 grams and a speed of 1000 m/s but despite its small mass it is difficult to stop.

LAW OF CONSERVATION OF MOMENTUM "The momentum of an object of an isolated system always remains constant is known as law of conservation of momentum."


Mass Weight 1. The quantity of matter in a

body is called its mass. It is the measurement of inertia possessed by a body. It is that property of a body which determines the acceleration produced in it under the influence of given force i.e a = F/m

2. Mass has no direction.

3. The mass of the body remains constant every where, whether it is measured at a point for away from the center of the earth or close to its centre.

1. Weight is the force with which earth attracts a body towards its centre. If the mass of the body is m and its acceleration due to gravity is g, its weight W is given by W = mg.

2. Weight is always

directed towards the centre of the earth.

3. The weight of body is not a constant quantity as its value is different at different distances from the center of the earth.

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Isolated System: The system which is not act upon the external force is called isolated system.Explanation: Consider a system consisting of two ball of masses m1 and m2 moving in straight line, with velocities u1 and u2 (u1 > u2). On colliding with each other they move with velocities v1 and v2.The total momentum of the system before collision = m1 u1 + m2 u2 -------------- (1) u1 u2

Now collision of the system

After collision the momentum of the system = m1 v1 + m2 v2 ---------- (2) V1 V 2

Combine both equations m1 u1 + m2 u2 = m1 v1 +m2 v2

Law of conservation of momentum m1 u1 – m2 v1 = m2 u2 – m2 v2

m1(u1 – v1) = m2(u2 – v2)

FRICTION: If a body is slide over to other the body of surface OR if a body is made to side over the surface OR If a body is made to slide over the surface of another body of motion is opposed by the force of friction due to roughness of the two surfaces. F œ RWhere "R" is reaction of body F = μ R-------- (1)

μ = F R

Meu (µ) is coefficient of friction.If normal reaction is equal to the weight of the block. R = mg .: W = mg F = μ mg


m1

m2

m1

m2

m1

m2

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Co-efficient of friction is constant for a given pair of surfaces. For a different pair it has a different value. Values of µ for some pair of surfaces are given in the table. Object ( dry surface) Co-efficient of friction

Between wood and woodBetween wood and stoneBetween metal and metalBetween wood and leatherBetween road and rubber tyre

0.30.40.20.40.7

ROLLING FRICTION: A spherical ball rolling it experience an opposite force called rolling friction. OR When a body rolls over the surface, the force of friction is called rolling friction.For Example: The rolling friction between steel surface is 1/100 of the sliding friction between these surfaces. Besides, in rolling friction the contact surfaces is much les than that in sliding friction. Advantages and Disadvantages of Friction:Advantages of Friction: Friction is very useful of our daily life. In the absence of friction motion would not have been possible. When we walk, we push the ground backward and the ground gives us a reaction in forward direction. This is possible because of friction. When we stop a moving car or bicycle, we again use the force of friction between the wheel and the road.Disadvantages of Friction: The main disadvantage of friction is that it produces heat in various parts of the machines there by some useful energy is wasted as heat energy. Similarly, cars, buses, and trains lose part of their energy is overcoming friction.Methods of Reducing Friction: Friction can be reduced by adopting the following methods.(i) The various parts of the machines which are moving over one

another are properly lubricated. (ii) In machines the sliding of various parts is usually replaced by

rolling and this is done by using bail bearing.(iii) Where sliding is unavoidable a thick layer of greasing material is

used between the sliding surfaces.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= (iv) The front of the fast moving objects e.g cars, aeroplanes are made

oblong to minimize air friction.

CHAPTER NO 6 STATICSTopics of the chapter:(a) Introduction of Statics (b)Resultant of Two Forces(c) Resultant of Two Forces at an Angle (d)Equilibrium(e) Torque or Moment of a Force(f) Condition of Equilibrium(g)States of Equilibrium (h)Centre of Gravity (i) Centre of gravity of Irregular Shaped Objects


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= INTRODUCTION OF STATICS:Definition: It is the study of the bodies at rest under no: of force, the equilibrium is called Statics.

RESULTANT OF TWO FORCES: Let us consider a body. Two forces F1 and F2 are equal in magnitude, are acting on it in opposite direction along the same line. The body remains at rest under the influence of these forces. If the forces were unequal the body would move towards the stronger one. The net effect of the forces is a single force which is called resultant of the friction of the forces. F1 F2

Equal forces acting on body

F1 F2

Unequal forces acting on body

The two forces may act on the body making certain angle with each other

F1

F

F2

Resultant force (F)

RESULTANT OF TWO FORCES ACTING AT AN ANGLE: In case of the forces can be represented in the magnitude and direction by two adjacent side of a parallelogram. The resultant force is a vector represented by the diagonal from the point of intersection. This is called the parallelogram of forces. In head-to-tail rule we draw force F1 from the terminal point of force F2. to get the resultant forces FR, we draw a vector from the initial point of the force F2 to the terminal point of the force F1. This is the same force as obtained from the parallelogram of forces


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= F1

F2

F1 FR

F2

EQUILIBRIUM: Two equal forces are acting on body in the opposite directions is called Equilibrium. When they are in rest or motion. If the two forces F1 and F2 are equal and opposite and acting along the same line. There are two types of Equilibrium.

(1)Static Equilibrium (2)Dynamics Equilibrium

(1) Static Equilibrium: The body forces acting remain same as in rest is called static equilibrium. Explanation: The book lying on a table as a book at a rest. The body is acting on the horizontal direction.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= (a) Two forces act upon the book, the force of gravity downward and equal force by the table upward.(2) Dynamics Equilibrium: The acting forces. There will in the motion state is called Dynamics equilibrium. The body is acting on the vertical direction to ward the earth. Two forces are not in equal. At torque is zero. Explanation: Now consider the jumping of paratroops from the areoplane. After jumping from the areoplane, the parachute is not opened for some time. During this period the paratrooper falls freely downward with acceleration due to gravity of earth. On opening the parachute, the acceleration of the paratrooper will start decreasing due to reaction of air on the parachute depends upon the velocity of the parachute. When this velocity decreases the reaction of air will also decrease. At a particular velocity the reaction of air on parachute becomes equal to the weight of the paratrooper. At this stage both the forces cancel the effect of each other and the parachute falls down with a uniform velocity. This is an example of dynamics equilibrium.(b) After a parachute opens and falls a certain distance, it moves downward thereafter with uniform velocity.

TORQUE OR MOMENT OF A FORCE: The turning effect of a force of body is called torque. Moment of force or torque may be rotates an object in clockwise or anticlockwise direction is called torque. The product of force and the moment arm of the force. Mathematically: τ = F × d Where " τ " is used for torque τ = N.m S.I unit of torque N.m For example: Consider the example of opening of a door. It is commonly observed that if a force F is applied at a point 'A' the door opens more easily than if the same forces is applied at point 'B' it is concluded that further the line of action of a force from the axis, greater is the torque. In


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= other words the torque depends on the distance between the line of action of the force and the axis of rotation of the body. However, the distance is the perpendicular distance between the axis and the line of action of the force and the axis. If the same force F is applied at point A, not in a direction perpendicular to the door, but in a direction which passes through the hinges, the door does not open. The torque is zero, because the perpendicular distance between the direction of the force and axis of rotation is zero. Thus the torque depends on the perpendicular distance between the axis of rotation of the body and line of the action of the forces. This perpendicular distance is called the moment arm. To the other factor on which the torque depends is the magnitude of the applied force. It is commonly observed that greater the magnitude of the force applied to the door at any particular distance from the axis of rotation, easier it is to open the door. From the above consideration we may conclude that the torque depends on two factors. (1)The magnitude of the applied forces.(2)The moment arm

CONDITION OF EQUILIBRIUM:

First of Condition of Equilibrium (Static Equilibrium): According to Newton's second law of motion, we know that if the net force acting on an object is zero the object has zero acceleration. If an object that is at rest or moves with a uniform velocity then the equilibrium is defined as "An object is in equilibrium when the object has zero acceleration" OR"An object is said to be in equilibrium if the sum of all the forces acting on it in one direction balances the sum of all the forces acting in the opposite direction."If two dimension x-axis and y-axis is equal to aero.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= ∑ Fx = 0 ∑ Fy = 0 ∑ it is symbol of sigma.Second Condition of Equilibrium: This condition net turning effect of forces acting on the object must be also zero. if body apply two equal but opposite forces at point x-axis and y-axis. ∑τ = 0STATES OF EQUILIBRIUM: There are three states of equilibrium, these are:

(1)Stable equilibrium (2)Unstable equilibrium (3)Neutral equilibrium

(1) Stable Equilibrium: "If a body returns back to its original position when it is slightly displaced, then the body is said to be in stable equilibrium" For Example: A book lying flat on a table is in stable equilibrium. In stable equilibrium, when the body is displaced, the centre of gravity is slightly raised and the weight of the body passes through base. (2) Unstable Equilibrium: "If a body not return to its original position when it is slightly displaced then the body is said to be its unstable equilibrium."For Example: A pencil placed vertically on table is unstable equilibrium. In unstable equilibrium, when the body is displaced slightly, the centre of gravity is slightly lowered and the weight of the body does not pass through base.(3) Neutral Equilibrium: "If a body is slightly displaced. It does not come back to its original position but occupies a new position similar to its original position, then the body on said to be in neutral equilibrium."For Example: If ball is pushed slightly to roll, it will not come back to its original position. The new position of the ball is similar to original position. In this case the centre of gravity is neither raised nor lowered but it remains at the same height. CENTRE OF GRAVITY: "The centre of gravity is defined as a point at which the whole weight of the body appears to act."The centres of gravity of regular shaped bodies are:(1) Sphere Centre of Sphere(2) Circular Plate Centre of plate (3) Uniform Rod Centre of Rod (4) Triangular Plate Intersection of Medians


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= (5) Cylinder mid Point of Axis

CENTRE OF GRAVITY OF IRREGULAR SHAPED OBJECTS: Centre of gravity shaped bodies is found by following rule. Centre of gravity lies below the point of suspension. Drill few holes near the edge of the plate. Suspend the plate by

passing nail through hole. A when the plate comes to rest draw vertical line

Again suspend the plate by passing nail through the hole B and when plate comes to rest draw the vertical line

As centre of gravity (CG) lines below the point of suspension, therefore it must be on the line. First line as well as on the second line. The only point common to both the lines is the point of intersection G. This must be the centre of gravity of the body.

CHAPTER NO 7 CIRCULAR MOTION AND GRAVITATIONTopics of the chapter:(a) Circular Motion (b) Uniform Motion (c) Centripetal Force (d) Centrifugal Force(e) Gravitation (f) Law of Universal Gravitation (g) Mass of Earth (h) Variation of g with Altitude

CIRCULAR MOTION:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= The Motion occur in body by rotational with axis is called circular motion OR If a body move with circular path is called circular motion.For Example:(1)Planets revolve round sun (2)Electrons revolve round nucleus(3)The Moon revolves round earth

In all the above examples, the force acting on the bodies changes the direction of velocity and not the magnitude of velocity.

UNIFORM CIRCULAR MOTION: If a body moves with constant speed in a circle, then it is called uniform circular motion. Suppose an object is rotating in a circle with constant speed as shown in fig: 7.1 x

z

y

Since the object is rotating with constant speed, therefore the magnitude of velocity (Speed) is constant but the direction of velocity is continuously changing which is along tangent at points x, y, z etc. Since the velocity is changing (due to change in direction and not the magnitude), therefore, the object is said to posses acceleration. This acceleration is called centripetal acceleration and is written as a, it is found that (1) ac is directly proportional to square of velocity, and (2) ac is inversely proportional to the radius of the circle. If m be the mass, v be the speed of the object rotating in the circle of radius r, then


ac = V2/r

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= (1)

The direction of this acceleration is towards centre of the circle or perpendicular to the direction of motion. CENTRIPETAL FORCE: From Newton's 2nd law, we know that force produces acceleration in its own direction. Thus centripetal acceleration is produced by a force having direction towards centre of the circle. This force is called centripetal force and is written as F According to the Newton's 2nd law F = ma Using the value of ac from eq (1) we get (2)

Suppose a ball of mass m is attached to one end of string and the other end is held in hand. If the ball is rotated in a horizontal circle with constant speed, then the hand is applying force on the ball through string towards the centre of the circle. This force is centripetal force. If the string breaks, then the ball will move along tangent.CENTRIFUGAL FORCE: According to the third law of motion the relation of the centripetal force pulls the ball outward. This outward relation force on us is called Centrifugal force. The magnitude of the centrifugal force is equal to the magnitude of the centripetal force but its direction is opposite. Suppose a ball of mass m is attached to one end of a string and the other end of the string is held in hand. If the hail is rotated with constant speed in horizontal circle, then the hand is exerting force on the ball forwards centre through string. This force is centripetal force. Since to every action, there is an equal and the opposite reaction. Therefore the ball is exerting an equal force on hand having direction away from the centre of the circle. This force is called centrifugal force. GRAVITATIONAL FORCE: When a body or mass of object or ball is dropped from the top of a building, it accelerates downward at 9.8m/s2 therefore a force must be acting on it is called the force of gravitation or gravitational force.LAW OF UNIVERSAL GRAVITATION: It was isolated by Newton in 1666, so it is some time says Newton’s law of universal gravitation. It is statement that “Every body in the universe attracts every other body with a force which


Fc = mV2/r

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= is directly proportional to the product of their masses and inversely proportional to square of distance between their centers”. Consider two spheres A and B of masses m1 and m2 with their centers at a distance r from each other, then according to the law of gravitation, the force of attraction F is A B

F

Then mathematically written as, F α m1m2 ------------------- (i)

F α 1/r2 ------------- (ii) Combine both equation, we yet F α m1m2/r2

F = G m1m2/r2 Where “G” is the constant of proportionality and is called gravitational constant. Its value is 6.67×10-11N.m2/kg2.MASS OF EARTH: The mass of earth can be determined by help of “universal gravitation law”. Let Me be mass of earth and R is its radius. When body of mass m is placed on the surface of earth, then according to law of gravitation, the force exerted by earth on the body is, m

According to universal gravitational law F = G m1m2/r2 F = G ME m/R2 ---------- (i) :. W= mg :. a = g Therefore F = mg mg = GMe m R2 g = GMe R2


M2M1

r

R ME

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Where “g” is acceleration due to gravity. g = GMe 1 R2 B. M. C

Now putting the value following in above formula Me mass of earth. g = 9.8 m/s2

R = 6.4×106m G = 6.67×10-11N.m2/kg2

Me = g R 2 G

Me = 9.8×(6.4×10 6 ) 2 6.67×10-11

VARIATION OF g WITH ALTITUDE: The value of “g” does not depend upon the mass of body. The acceleration due to gravity depends upon the distance of the body from the centre of earth. Centre

Equatorial Radius

If distance from the center of the earth is increased, the value of g will be decreased. The value of g at the pole is greater than at equator between the earth is not a perfect sphere. Its equatorial radius is greater than the radius at the pole. If the distance is equal to twice the radius of the earth from its surface. Its value will decrease to one2 ninth.


Me = g R 2 G

Me = 6×1024 kg

Equatorial Radius


CHAPTER NO 8 WORK, ENERGY AND POWER

Topics of the Chapter: (a)Work (b)Energy(c) Kinetic Energy and Potential Energy (d) law of Conservation of Energy (e) Need to Conserve Energy(f) Power

WORK: It is done when a force produces displacement in body OR The product of force and displacement is called work Mathematically W= F × d W= F × S


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= It is vector quantity. Its components of force with direction

When force and distance are not in the same direction but force makes 1k with the direction of motion then the work is calculated by multiplying component of force along the direction of motion and distance. W= F Cos θ × S or W=FS Cos θ

In S.I System, the unit of work is joule. It is defined as “If force of 1 N moves body through 1 m in the direction of force, then the work is said to be 1 J.” ENERGY: “The ability of doing work is called energy.” The unit of energy is same as that of work i.e. joule.There are various forms of energy. For example; chemical energy, electrical energy, mechanical energy, heat energy, solar energy, nuclear energy etc. Here we shall study mechanical energy which may be kinetic or potential energy.KINETIC ENERGY AND POTENTIAL ENERGY:Kinetic Energy: “The energy due to motion of body is called kinetic energy.”Let us calculate the kinetic energy of a body of mass m moving with velocity V. Suppose the body is at rest on frictionless surface. A force F acts on the body and moves it through a distance S in its own direction, such that the final velocity of the body becomes V.


W=Fs ------------ F

S

Fy

F

θ Fx

F Cosθ S

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Now W= F× S, But F= ma hence W= ma × S

Let us calculate S separately. Vi =0 Now Vf = V Vf

2 - Vi 2 = 2as

S = ? or V2 – (0)2 = 2as or V2 = 2as or S = V2/a. Using it in eq W = ma × S, we get W = ma× V2/2a or W = 1/2 mV2

Since this work is done by the force upon the body, therefore the body possesses same kinetic energy. Hence K.E = ½ mV2 Thus

(1)K.E is directly proportional to the mass of the body, and (2)K.E is directly proportional to the square of velocity

Potential Energy:“The energy possessed by a body by virtue of its position is called Potential energy.”If a body of mass m is lifted through a height h against the force of gravity mg, then the work on the body is mgh. This work is stored in the body as its potential energy. Hence P.E = mgh In this formula h is the vertical height. The body may be carried from ground to the height h through any path, the P.E remains same i.e. mgh.LAW OF CONSERVATION OF ENERGY:Statement: “Energy can neither be created nor destroyed but it can change from one form to another form” Let us verify law of conservation energy in the case of mechanical energy (kinetic and potential).


W=Fs ------------ F V S

m m

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Suppose a body of mass m is at which is height h above the ground level C, B is a point distance x below A.

At A the body is at rest.Therefore K.E = 0 P.E = mgh, therefore, the total energy E is E = K.E + P.EE = 0 + mgh or E = mgh (1) If the body is allowed to fall, then h decrease therefore P.E decrease but since due to acceleration g, the velocity increase therefore the K.E increases. Hence it can be said that P.E is converted into K.E When the body passes through B, then new height is (h-x). let us find velocity V at B by using the equation of motion. Vf

2 - Vi 2 = 2as

Or V2 – (0)2 = 2gx where a = g and s = x V2 = 2gx Hence at point B K E = ½ mV2 = ½ m × 2gx = mgx& P.E = mg (h-x) = mgh – mgxAdding them we get the total energy at B as E = K.E + P.E Or E = mgx + (mgh – mgx)Or E = mgx + mgh – mgx Or E = mgh This is same as total energy at A which is given by equation (1). Thus when P.E is converted to K.E “The total energy remains constant”Hence the Law is verified.POWER:


A

x B

h

h-x

C

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= The rate of doing work is called power or the ratio between the working by the time is called Power or work done in a unit time is called power. It is scalar quantity. Its formula is P = w/t .: W = F×d Or P = F×d/t The S.I unit of power is Watt. 1 watt = Joule/timeWatt: Power is joule per second is called Watt.Bigger unit of power is 1 KW = 103 W 1 MW = 106 W The one horse power is equal 1 hp = 746 Watt

CHAPTER NO 9 MACHINESTopics of the Chapter:(a) Introduction (b)Mechanical Advantage and Efficiency(c) Kinds of Machines

INRODUCTION: There are many devices which helps us in doing work in a convenient manner. All these devices are called machines.MECHANICAL ADVANTAGE AND EFFICIENCY: Some important terms used in machines are defined below:Effort: It is the force applied on the machine. It is denoted by P.Load: It is the weight lifted by machine. It is denoted by W.Mechanical Advantage (MA): The ratio of load to effort is called mechanical advantage.Therefore Mechanical Advantage = load/effort MA = W/P (1) MA has no unit.Input: The work done on the machine is called input. If effort P acts through a distance d, then Input = Pd (2) Output: The work done by the machine is called output. If load W is lifted through a height h, then


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Output = Wh (3)Efficiency: The ratio of output to input is called efficiency of machine. Efficiency = Output/Input Efficiency is measured in percentage. Hence

(4)

Using equation (2) and (3) we get Efficiency = Wh/Pd × 100 (5) Machines do not create any energy for us. It does same work what we put into it. Actually out is less than input because some energy is used up in overcoming friction which exists between various parts of machine. Thus the efficiency of machines is always less than 100 %. A machine is said to be ideal if output is equal to input. For this machine the efficiency is 100 %. Hence for ideal machineOutput = Input Wh = PdOr W/P = d/h or MA = d/h (6)Thus Mechanical Advantage depends upon the distance through which effort P acts the height through which load W is lifted.

KINDS OF MACHINES: All machines consist of one or more of the following Six simple machines. (a) Lever (b) Pulley (c) Inclined Plane (d) Wedge (e) Screw (f) Wheel and Axel

(a)Lever: It is a simple machine which consists of a rigid bar capable of turning about a fixed point called its fulcrum. Load W is lifted by lever by applying the effort P. The perpendicular distance between effort P and function is called effort arm. The perpendicular distance between load W and fulcrum is called weight arm or load arm.Levers are three kinds depending upon the position of effort.Lever of 1st kind: Fulcrum F is between P and W.


Output × 100Efficiency = Input

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= For example, balance, handle of a pump, a pair of scissors, see saw are examples of it. Lever of 2nd kind: Load W is between fulcrum F and effort P. The door, the nut cracker, punching machine and oar used in rowing, are examples of second kind of lever.Lever of 3rd kind: Effort P is between fulcrum F and load W. Human fore arm, upper and lower jaws in the mouth, a pair of forceps, etc are examples of 3rd kind of lever. In all kind of lever Torque of effort = torque of load i.e. Effort × effort arm = Weight × weight arm P × BC = W × AB Or W/P = BC/AB Or MA = Effort arm/Weight arm (7)

(b) Pulley: A pulley is a grooved wheel supported in a frame, Called block such that wheel can turn about an axle in the block. The pulley can be suspended from a fixed beam by means of a hook. A rope can pass over the pulley. The pulley can be used in two ways. (1) Fixed Pulley: The block of the pulley is fixed to the ceiling. Load W is tied to one end of the rope and effort P is applied as the other end. If we neglect the weight of the rope and friction. Then W × OB = P × OA As OB and OA are equal, therefore they cancel out Hence, W = P Or W/P = 1 or MA = 1 (8)The effort applied P is equal to the weight W. This pulley is used only to change the direction of force. W is lifted upward by applying effort P in the downward direction which is a convenient direction to apply force. (2) Moveable Pulley: In this case the block and the pulley both are moveable. The weight W is tied to a hook in the block of moveable pulley and effort P is applied at the force end of the rope. Two segments of the rope are lifting W. The tension in each segment is P. Hence W = 2P Now, Mechanical Advantage = W/P using W = 2P, we get MA = 2P/P


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Or MA = 2 (9)MA is 2 which mean a load of 100 N can be lifted by an effort of 50 N.

(c) Inclined Plane: Inclined plane is a plane surface inclined at certain angle with the horizontal. It is used in raising heavy loads. The load W is lifted through a height h by applying effort P through a distance l along the place. Output = Input Wh = P × l Or W/P = l /hOr MA = l /h (10) Since h/l = Sin θ Hence Therefore l /h = l /Sin θ MA = l /Sin θ (11)Thus the smaller the angle θ, the greater is the mechanical advantage.

(d) Wedge: It consists of two inclined plane put together. It is used to split wood into pieces.Let an effort P be applied on the top of the wedge placed on a log of wood. The load in this case are the forces R1 and R2 each equal to R acting perpendicular to the inclined planes of the wedge.The forces P, R1, and R2 can be represented by the sides of a triangle xyz such that xy represents P yz represents R1 and yz represents R2 since R1 = R2 = R = load, therefore MA = load/effortOr MA= R/P Or MA = zx /xy As Δ’s xyz and and ABC are similar and zx/xy = AC/BC Therefore MA = AC /BC

or (12)

(e) Screw:


Length of inclined surface of the wedgeMA= Thickness of the wedge

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= It consists of a threaded rod with a head, called the screw head. The distance between two adjacent threads is called its pitch, applied at the screw head, the screw moves forward into the wood through a distance equal to its pitch h. if d be the radius of screw head then the effort P moves through a distance 2πd. If there is no loss of energy due to friction, then Output = Input W× h = P × 2πd W/P = 2πd /hOr MA = 2πd /h (13)

Screw Jack: It is a simple machine used to lifted a car or other automobile when need arises. The car or automobile of weight W is placed on the platform provided for this purpose. The pitch of the screw is h. The effort P is applied at the handle H. When effort moves through a distance 2πd (one rotation) where d is the length of the rod, the load W is lifted through a height h. For an ideal case (no friction). Output = Input W/h = P × 2πd W/P = 2πd /h Or MA = 2πd /h (14)

(f) Wheel and Axle: A wheel with larger radius (R) and another with smaller radius (r) are fixed on the same shaft and are called wheel and axle respectively. It is often used to lifted bucker of water from the well.The shaft is held in clamps so that it can rotate freely. The effort P is applied at the rim of Wheel of radius R while the load W is lifted by a string wound round the axle. For one complete rotation, the effort moves through a distance 2πR while the load is raised through a distance 2πR. If friction is neglected, then Output =Input W × 2πr = P × 2πR W/P = 2πR/2πr Or W/P = R/r Or MA = R/r (15)



CHAPTER NO 10 MATTERTopics of the Chapter:(a) Introduction(b)Molecular Kinetic theory of Matter (c) Brownian Motion(d)States of Matter (e) Elasticity(f) Stress (g)Strain(h)Hooke’s Law (i) Young’s Modules(j) Fluids (k)Pressure (l) Pressure in liquids(m) Pascal’s Principle (n)The Hydraulic Machines (o)Atmospheric Pressure(p)Barometers (q)Archimedes Principle (r) Buoyancy and floating of bodies

INTRODUCTION: Matter exists in these states. These states are solid, liquid, and a gas. Temperature and pressure may change the state of matter. For example, ice is solid. When heated it is converted into liquid (water). On further heating it is converted into gaseous state (steam). The existence of these states of matter can be explained on the basis of kinetic molecular theory of matter.

MOLECULAR KINETIC THEORY OF MATTER: According to this theory, matter consists of molecules. A molecule consists of one or more atoms. The molecules are in some state


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= of motion, therefore they possess kinetic energy. The motion can be translational, vibrational and rotational. The molecules of a substance attract each other with a force which increases with the decrease of distance between them. When a substance is heated, the molecular motion increase the motion which is increased may be transnational, vibrational or rotational depending upon the state of matter.

BROWNIAN MOTION: The fact that molecules are in motion was first found by Robert Brown in 1827. He observed that Pollen grains suspended in water were constantly moving in a Zig Zag path. This motion was due to collisions of water molecules with pollen grains. This confirmed that water molecules were also in random motion. This random motion of tiny particles is called Brownian motion.

This Brownian motion is seen whenever very small particles are suspended in a fluid (liquid or gas) medium. For example, smoke particles in air also show Brownian motion.

STATES OF MATTER:Solid: The molecules of solids are held firmly to one another by some force of attraction. They simply make vibratory motion about their mean positions and do not move away from each other. Solids have definite shape and can not be compressed easily. As the temperature of a solid is raised, its molecules vibrate with greater amplitude. At a certain temperature, called the melting point, force of vibrations overcomes the binding forces and the solid is converted into liquid. Liquid: The attractive forces between the molecules of liquid are less strong than in solids. Liquid molecules are no longer held in fixed position but can slide over one another. The molecules of liquid are arranged in fixed pattern; therefore the liquids do not have definite shape. They occupy the shape of the container in which they are placed. The surface of a liquid is always in level because the molecules at the surface are attracted inward by the other molecules. When a liquid is heated, its molecules gain more kinetic energy. At a certain temperature, the kinetic energy is so large that it overcomes


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= the attractive force between the molecules. The molecules escape from the surface and the liquid is converted into gas. Gas: The molecules of gas are at a large distance from each other, therefore the force between the molecules of gas is negligible. The molecules of the gas are constantly in random motion making collision with each other and with the walls of the container. Like solids, gases do not have definite shape and like liquids, they do not have definite volume. ELASICITY: When force is applied to a rubber wire, it is stretched. When the force is removed, it regains its original shape and size. “The Phenomena of returning to original shape and size after the force is removed, is called elasticity.” If force is applied to a meter rod, it bends. When force is removed, it again becomes straight. If the force is increased, then at a certain value of force, it breaks. Thus there is a limit to the applied force form which the rod recovers its original shape when the force is removed. This limit is called elastic limit. After crossing this limit, the material never gains its original shape even when the force is removed The elastic behavior can be explained on the basis of kinetic molecular theory of matter. In solids, the force of attraction between the molecules is very large. Thus when the supplied force is removed, this force of attraction between the molecules brings the body back its original shape. A body is said to be more elastic if it shows less change even when large force is applied to it. Thus steel is more elastic than rubber. STRESS: Suppose a force products change in length of rubber wire if cross sectional area is doubled, then double force will be required to produce same change. “The opposing force that resists any change, acting per unit area, is called stress.”

For example, if On area A, force is = F When on unit area, the force is = F/A, HenceStress = F/A = Force/ area is denoted by Greek letter sigma (σ) Hence σ = F/A (1) Its unit is N/m2

STRAIN: Stress can produce change in shape, length or volume. This change is called strain.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= “The change in unit length is called longitudinal strain”For Example, If the length L, Changes by = ΔL Then unit changes by = ΔL /L, Hence Longitudinal strain = ΔL /L = change in length / original length is denoted by Greek letter epsilon (ε), Hence ε = ΔL /L (2) it has no unit.HOOKE’S LAW: It states that within the elastic limit, “Stress is directly proportional to strain.” i.e. Stress α strainIf a graph is plotted between stress and strain for a steel wire, then it is a straight line upto point χ. In this region stress is proportional to strain and the material is elastic. If the stress is removed, the wire regains its original length.

Plastic Region Breaking point

Strain

Stress If the stress is applied beyond elastic limit, the change becomes permanent and the material is said to be in the plastic region. The point at which material becomes plastic is called elastic limit or yield point. The material breaks at a certain point, called the breaking point.YOUNG’S MODULES:With in elastic limit Stress / Strain = ConstantThe constant is called Modules of elasticity.“The ratio of normal stress to longitudinal strain is called Young’s Modules of elasticity.”Thus Young’s Modules Y= Stress / longitudinal strain Or y = σ / ε Using equations (1) and (2), we get y = F/A / ΔL / Lor y = FL / A ΔL (3)


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= FLUIDS: Fluids (including both liquids and gases) are the substances that flow. A fluid acquires the shape of the container in which it is put. Fluid put in a container exert force perpendicular to the walls of the container. If this were not so, any sideways force by a fluid on a wall (action) would be met with an equal force on it by the wall (reaction) which would cause the fluid to move constantly parallel the wall. Since this does not happen, therefore the fluid exerts force perpendicular to the wall.PRESSURE: The perpendicular force acting on unit area of a surface is called pressure. If the area A, the force is F then on unit area, the force is F/A hence, Pressure = F/A = force/Area P= F /A (4) The unit of pressure is also N/m2 called Pascal (Pa), such that 1Pa = 1 N/m2, henceWhen one Newton force acts on one m2, the pressure is said to be 1 Pascal. The bigger unit is kilo Pascal (1KPa 2 = 1000 Pa 2).PRESSURE IN LIQUIDS Let us calculate the pressure at the bottom of liquid contained in a glass.Consider an imaginary Cylinder of liquid inside the liquid. The lower circular cross sectional area A is depth h below the surface. The volume of the liquid in the cylinder = Ah. If ρ (Greek letter rho) be the density of liquid, then Mass / volume = density Or m / Ah = ρOr m = ρAh. Hence Weight mg = ρ. Ahg This is the force acting normally at the area A. Since Pressure = Force / Area, thereforce P = ρ Ahg / A Or P = ρhg (5)Thus pressure at point inside liquid depends upon 1) The height from the surface, and 2) The density of the liquidFor Example, A swimmer experiences more pressure at a greater depth than at a lesser depth. Similarly a more dense liquid exerts more use pressure at a point in the liquid than a less dense liquid exerts at the same point. PASCAL’S PRINCIPLE:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Pascal’s Principle says that“Liquid transmits pressure equally in all directions.”Pascal’s Principle can be verified by an experiment. Consider a vessel containing four pistons. This vessel is filled with water. If a force is applied inward through a certain distance on one piston, then the remaining three pistons move outward through some distance. Thus the liquid transmit pressure equally in all directions.

THE HYDRAULIC MACHINES:The following machines are deviced on the fact that liquid transmit pressure equally in all directions.The Hydraulic Brake System:The hydraulic brake used in a car or bus etc.It consists of a matter cylinder joined by tubes to four small cylinders, one for each wheel. They are called brake cylinders. The tubes contain brake oil. When the brake pedal is pressed, the pressure is exerted on the oil. This pressure is transmitted equally to the brake cylinders through the oil. This pressure causes the piston in each brake cylinder to move outward. The outward motion of the piston causes the brake shoe to tough against the rotor and hence the friction stops the wheel. When the brake pedal is released, the spring which connects the two brake shoes contracts, due to which the brake shoe are pulled inward and the wheel gets free.Hydraulic Lift: In hydraulic lift a narrow cylinder A is connected with a wider cylinder B. It is filled with incompressible fluid. When pressure is applied at A in the downward direction, then according to Pascal's Principle, it is transmitted equally to B. The piston B which acts as platform therefore moves upward and the heavy load placed over the plat from is lifted. Hydraulic Press:It is similar to hydraulic lift with the difference that the piston B used to lifted heavy object is provided with a rigid roof. When the piston B moves upward, it compresses any object placed between the rigid roof and the piston. It is used to compress cotton into compact bale, powdered materials into compact solids etc Pressure in gases:Suppose a gas is contained in a vessel. According to kinetic theory, the molecules of gas are in random motion. The molecules move freely inside the vessel and make collision with each other and with the wall of container. The continuous collisions of molecules with the wall of the vessel accounts for the pressure of the gas. ATMOSPHERIC PRESSURE :


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= We live the bottom of deep sea of air called atmosphere. The major gases in air are nitrogen and oxygen. The atmosphere due to its weight exerts pressure on the surface of earth and on every thing on earth. This pressure is called atmospheric pressure. At sea level atmospheric pressure is about 105 Pa (105N/m2).Barometers: It is device used to measure atmospheric pressure is called barometer. Different types of barometer are below;

Mercury Barometer: it is simple barometer used to measure atmospheric pressure in the laboratory.

Aneroid Barometer: it does not contain liquid. It consists of corrugated steel box partially evacuated of air.

CHAPTER NO 11 HEATTopics of the Chapter:(a) Introduction(b)Nature of heat(c) Temperature(d)Transfer of heat(e) Thermal Conductivity(f) Gases laws(g)Specific heat(h)Law of heat exchange

Introduction: When a piece of iron is placed on fire, it becomes hot. It means, it has taken something from fire. This something is called heat.Nature of Heat: Heat is the transfer of energy (energy in transit) from one body to another due to the temperature difference between the two bodies. When a body absorbs heat, its internal energy increases and when it loses heat,


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= its internal energy decreases. Internal energy is the sum of all the kinetic and potential energies of all the molecules of the body. Temperature: "Temperature is the degree of hotness or coldness of a body." According to kinetic molecular theory, the molecular of substance have various values of kinetic energy, some molecules have large K.E and some molecules have small K.E. "The average kinetic energy of molecules of a substance determines the temperature of the substance."Thermal Conductivity: The ability of substance to conduct heat energy is called thermal conductivity. Consider a metal block a length ∆L and area cross section such that its one end is constantly maintained at a lower temperature T1 and other end at a higher temperature T2 .If heat ∆Q conducted from hot end to the cold end in end in ∆t seconds, then it is end that, ∆Q α A ∆Q α (T2- T1) ∆Q α ∆t ∆Q α 1/∆L Combining them we get ∆Q α A (T2- T1) ∆t/∆L ∆Q = constant A (T2- T1) ∆t/∆L ∆Q = KA (T2- T1) ∆t/∆L -------------- (i)

If (T2- T1) = ∆T, then ∆Q = KA ∆T ∆t/∆L ------------------ (ii)

The constant K is called thermal conductivity of the material of different materials have different values for K A = 1 m2

∆L = 1 m Area and length is equal to one meter cubic of the substance.∆T = 1 C◦ ∆t = 1 sec then from equation (2) we have ∆Q = K × 1 × 1×1/1∆Q = K

The thermal conductivity is the quantity of heat conducted per second per cubic meter of a substance whose opposite faces are maintained at a temperature difference of 1 C.

Thermal Expansion of solid:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= The solid substances are expanding or increase in size by heating is called thermal expansion. For example: plastic jar expand on heat during summer it means that solid is heated its temperature rise and its molecules start vibrating with greater amplitude. Due to this, the average distance between the molecules increase and the solid expands.There are two types of thermal expansion.Linear thermal Expansion: When a metal rod is heated its length increase, is called linear thermal expansion.Consider a metal rod having length L. when the temperature is increase by ∆T, let the increase in length be ∆L it is found that Change in length (∆L) is directly proportional to original length (L). ∆L œ L → (1)Change in length (∆L) is directly proportional to change in temperature (∆T). ∆L œ ∆T→ (2)Comparing equation (1) & (2), then we get ∆L œ L∆T --------- (3)The constant œ is called co-efficient of linear expansion of the material rod. Then equation (3) can be written as

œ = ∆L/ L∆T ------------- (4)

Volume thermal Expansion:When a block is heated its volume increase is called volume expansion. If the volume V increases by ∆V when temperature is raised by ∆T then it is found that:Change in volume is directly proportional to the original volume. ∆V œ V → (1) Change in volume is directly proportional to the change in temperature. ∆V œ ∆T → (2) Comparing eq: (1) and (2), we get ∆V œ V∆T ∆V = β V∆T → (3) β = ∆V/ V∆T

Gas Laws: The behaviour of a gas is determined by physical quantities like pressure, volume, temperature and mass of the gas relation between two of variable, keeping the other variable constant are caused gas laws.

Boyle's Law:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= "This law state that volume of a given mass of a gas is inversely proportional to pressure. The temperature of the gas was kept by constant." Mathematically; it can be written as V œ 1/p V = 1/p (constant) Or V = k/p PV = k Or PV = Constant"Boyle's law can be defined as product of pressure and volume of a given mass of a gas is constant. Its temperature is kept constant." Boyle's Law by Graph: If we put a graph for different values of same mass of the gas we get hyperbolic as shown in the figure. The shape shows that if pressure of the gas is increased the volume will decrease and vice versa.

Charles's Law: "This law states that volume of a given mass of a gas is directly proportional to temperature. Its pressure of gas is constant." Mathematically can be written as V œ T V = T constant V/T =ConstantCharles's Law by graph: If graph is plotted between different values of volume and absolute temperature the gas at constant pressure. We obtained straight line, therefore we can say that volume and temperature change correspondingly. If this graph is produced in the backward direction then of observed that at temperature volume is not zero but it become zero at -273K. Generally the gases are liquefied before reaching to the temperature -273cº. The temperature -273cº is taken as zero on Kelvin scale of temperature. The zero is called absolute zero.



General Gas Law Or General Gas Equation General gas law is the combination of Boyle's law and Charles's law According to Boyle's law V œ 1/p (Temperature constant)

According to the Charles's law V œ T (Pressure constant) Combine both V œ T/p V = T/p constant PV = T constant or PV/ nT = constant → PV/nT = R PV = nRT where n is number of moles and R is universal gas constant, its value is 8.314 Joule /mole k

Specific Heat Capacity: Statement: "Amount of heat required to raise the temperature of unit mass by one Kelvin".Explanation: It is found experimentally same amount of different substance require different quantity of heat to raise their temperature by 1K or 1cº due different number of molecules. Mathematically it can be written as ∆Q œ m and ∆Q œ ∆T ∆Q œ m ∆T By removing sign of proportionality ∆Q = C m ∆T Where C is constant and depends upon the nature of material. This constant "C" is known as specific heat capacity or simply specific heat.

C = ∆Q_



m∆T Unit of specific heat is J/ kg K.Law Of Heat Exchange: When hot and cold bodies are placed in contact, the hot body loses heat and the cold body gain heat till the two bodies arrive at the same temperature. In no heat is lost to the surroundings or gained from the surroundings, then heat lost by the hot body is equal to the heat gained by the cold body. Thus the law of heat exchange says that Heat lost = Heat gained

This law is used to measure the specific heat of a substance by the method of mixture.

CHAPTER NO 12 WAVES AND SOUNDTopics of the Chapter:(a)Oscillation (b)Simple Harmonic Motion (c) Wave motion (d)Characteristic of Wave(e) How sound is produced (f) Characteristic of Sound(g)Echo

Oscillation: A motion which repeats itself in equal intervals of time is called periodic motion.If a body in periodic motion moves back and forth along the same path, then the motion is called vibratory or oscillatory.

Simple Harmonic Motion: The force exerted by spring on the mass is called restoring force. If F be the restoring force and at a certain instant if the mass be distance x away from its mean position, then according to Hooke's law, under elastic limit we have Fα – xOr F = Kx – xOr F = - Kx (1)


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Using Newton's 2nd law, we have ma = - Kx where K is constant is called spring constant a = - K/m x (2) or a = - (Constant)x both K and m are constantor a = (Constant)x-x or aα – x (3)Thus (1)Acceleration is directly proportional to displacement, and (2)Acceleration is directed towards mean position A vibratory motion having above two properties is called Simple Harmonic Motion (S.H.M). The above two properties are called characteristics of S.H.M Let us define certain terms used in connections with S.H.M.(1)Vibration: One completes trip is called Vibration.(2)Time period (T): The time of 1 Vibration or 1 Oscillation is called

time period.(3)Frequency: The number of vibrations made in 1 second is called

frequency. In S.I system, its unit is Vib/ s or Cycles or hertz.

Since In T seconds, number of vibration = 1

Therefore in 1 second, number of vibration = 1/ T. Hence f = 1/ T (4) (4) Displacement(x): The distance from mean position is called displacement.(5) Amplitude (x o): The maximum distance on either side from mean position is called amplitude. The mass attach to the spring performs S.H.M with the time period given as

Since f = 1/ T, therefore

Wave Motion: When we dip a pencil into a tub of water, the molecules of water below the pencil are disturbed. This disturbance moves from molecule to molecule with same speed. This disturbance is called wave. Since the disturbances moves with same speed in all directions, therefore the molecules which start to vibrate at a certain instant lie on a circle. That is why water waves are circular. It may be noted that the water molecules


T = 2π √m / K

T = 2π √m / K

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= which start to vibrate at a certain instant that water molecules simply make up and down motion when the wave (disturbance) passes through them. The water molecules do not move along with the wave. Suppose one end of a rope is tied to a wall and the other end is held in hand. If we disturb the end which is held in hand by jerking it, then this disturbance (wave) will move from particle to particle along the rope. The disturbances is moving along the rope is called a wave.Transverse Wave: "The wave in which particle of the medium vibrate perpendicular to the direction of motion of wave, is called transfer wave."For Example, Water waves and waves produced in a string are transverse waves. In transverse waves, the particles of the medium above mean level are said to form crests and the particles below mean level are said to form troughs.Longitudinal Waves: "The wave, in which the particles of the medium vibrate parallel to the direction of motion of wave, is called longitudinal wave."For Example, in a spring longitudinal waves are produced. The particle of the spring, vibrate parallel to the direction of motion of wave.Characteristics of a Wave: There are certain terms which are common to both types' waves. They are the frequency (f), the time period (T), the amplitude (A), wavelength (λ) and wave velocity (v). let us now define these terms.Frequency (f): The number of vibrations made by any particle of the medium in 1 second or the number of waves generated by a source in 1 second is called frequency. Its unit is vib/s or cycle/s or hertz. Time period (T):The time taken by the particle of the medium to complete 1 vibration is called time period. It found that f = 1/ TWave length and Amplitude:A transverse wave can be represented by the curve. The horizontal line represents the mean position of the particles of the medium. Particles above mean level form crests and particles below mean level from troughs.The wave length is defined as under:"The horizontal distance covered by the waves during one vibration of the particle of medium, is called wave length." ORThe distance between two successive crests or two successive troughs, is called wave length.



It is defined by the Greek letter λ (Lambda). The amplitude is defined as under:"The distance between the crest and the normal position or the distance between the through and the normal position is called amplitude. It is denoted by A."Wave Velocity (V): "The distance covered by the wave in 1 second, is called wave velocity." It is denoted by V.A very simple relation exists between wavelength, time period and velocity of a wave. Let us find this relation. We know that Velocity = Distance / time Since in the time period T, the wave covers distance λ, therefore, the above equation can be written as V= λ /Tor V= λ x 1/T Since 1/ T = f, therefore V= λ x f or V = fλ

Stationary Waves: "When two waves having same frequency and amplitude but traveling in opposite direction combine, stationary waves we produced." When a stretched string a fixed from both ends is plucked from centre or 1/4th of its length or 1/6th of its length, and released then two waves are produced which move towards fixed suppose. After reflection from supports when they combine with each other, stationary waves are produced. The points which remain at rest (Points of destructive interference) are called notes.The points which vibrate with maximum amplitude (points of constructive interference) are called antinodes.The distance between node and next anti-node is 1/4th of the wave length (λ/4).

How sound is produced: Sound is a form of energy which is produced by the vibrating body. When a body vibrates, it produces waves in the medium. When these waves reach our ear the sensation of sound is produced.Audible Frequency Range:Our ear can hear only those sounds whose frequency is between 20 Hz and 20000 Hz. That i, the ear can not hear the sound if as frequency is


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= less than 20 Hz or greater than 20000 Hz. A sound of frequency is greater than 20000 Hz can be produced but human ear can not detect it because ear drum can not vibrate with such a high frequency. Sound having frequency above 20000Hz is called ultrasonic.Velocity of Sound:We know that during rainy seasons the flash of lightening is seen earlier than the thunder. This is been use the velocity of light is very very large as compared to the velocity of sound. This observation can be used to find the velocity of sound.Consider two stations A and B at a distance of 8 to 10 km from each other in open space. An observer is present at each station with a stop watch and a gun. Each observer starts the stop watch when the flash is seen and stops when the sound is heard. The time measured by each stop watch in the time which the sound takes to travel the distance between two stations.If t1 to t2 times measured by the two observers, then the average time t = (t1 + t2) / 2 If S be the distance between two stations, then the velocity of sound is given as V = s/t The velocity of sound in air at O C is 330 m/s The velocity of sound in water is = 1450 m/s The velocity of sound in iron is = 5130 m/s

CHARACTERISTICS OF SOUND: There are two types of sounds called the musical sound and noise. In musical sound there is regularly between the vibration of frequency and amplitude where as in noise, there is abrupt change is frequency and amplitude. A musical sound has following characteristics. Loudness: Loudness of sound depends upon intensity. The intensity of sound is the energy crossing unit area held normally, in unit time. Loudness depends upon the following factors.(1) Area of vibrating object: "The larger the area of a vibrating objects,

the louder is the sound produced."(2) Amplitude: The greater the amplitude of the vibrating objects, the

louder is the sound produced.Pitch of Sound: "The characteristic of sound by which a shrill sound can be distinguished from a grave sound, is called Pitch of sound."Pitch depends upon the frequency. The higher the frequency, the higher is the pitch and shrill is the sound. The lower the frequency, the lower is the


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= pitch and grave is the sound. A disc capable of rotation about an axle has holes of equal sizes and equally spaced at its boundary. A rubber belt passes over the axle of the disc and also over a wheel which can be rotated by a handle.Take a long rubber tube having its one end connected to a compressor and the other end is connected to a metallic jet. Direct the get of compressed air onto the holes. Rotate the disc with handle when the hole comes against the jet, the air passes through it and produces disturbance (wave). As the speed of rotation of disc increases, the number of times the air passing through the holes, also increases and hence the frequency of sound eaves increase due to which the pitch of sound rises. Echo: "The sound heard after reflection from a surface, is called echo." For normal human after ear, the effect of a sound remains for about 1/10th of a second. Two sounds produce in this interval will not be heard as separate sounds.The echo of sound can therefore be heard only if it arrives the car in time 1/10 second or more. Suppose the echo of clapping is heard immediately while standing at certain distance from a cliff or wall or a building. If d be the distance of the cliff or wall or building from the person and V be the speed of sound then the distance 24 must have been covered by sound in time 1/10 seconds. Hence Speed = distance covered by sound / time taken by sound Or V= 2d/1/10 Or 2d = V×1/ 10.

CHAPTER NO 13 PROPAGATION AND REFLECTION OF LIGHT

Topics of the Chapter:(a)Rectilinear Propagation of Light (Path Of Light)(b)The Pinhole Camera(c) Reflection of Light(d)Laws of Reflection (e) Image Formed by a Plane Mirror (f) Spherical Mirrors(g)Reflection and Formation of image by a concave mirror (h)Reflection and Formation of image by a convex mirror (i) Mirror Formula (Equation for Spherical mirror)


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Rectilinear Propagation of light (Path of light):Rectilinear propagation of light means light travels in a straight time. If an opaque object is placed in the path of light, its shadow is formed behind the object. This shows that light travels in a straight line Image: The image of an object can be real or virtual.(1) Real Image: The rays starting from a point if really meet at some

other point, then the other point is called real image of the 1st point. Real image can be obtained on the screen.

(2) Virtual Image: The rays of light starting from a point if appear to meet at some other point, then other point is called virtual image of the 1st point.

Virtual image can not be obtained on the screen. It should be remembered that "AT LEAST TWO RAYS ARE RQUIRED TO CONSTRUCT AN IMAGE."The Pinhole Camera: It works on the principle of rectilinear propagation of light. It was invented to observe the eclipses of the sun without damaging the eye. It consists of rectangular box having a very small hole on one side and frosted glass plate or photographic film on the other side. The box is covered with a dark cloth.The pinhole camera forms real and inverted image of the object. A narrow pencil of rays starting form point A passes through the pinhole O and illuminates a small area at A. similarly, a narrow pencil of rays staring from C illuminates the small area at C. in this between A'C'. Thus a real and inverted image A'C of the object AC is formed on the photograph film.Reflection of Light:When light speeding from a source in one medium, falls on the surface of another medium, part of light is sent back in the same medium. This property is called reflection.Law of Reflection:When light traveling in one medium strikes the surface of another medium, a part of it is reflected back in the same medium. Mirrors and highly polished surfaces reflect the light strongly and the images of the objects formed by reflection obey the two laws is called the laws of reflection.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= AO is called incident ray OB is called reflected ray point O is called point of incidence. The perpendicular on the mirror from O is called normal.LAON = Li is called angle of incidence, and LBON = Lr is called angle of reflection.Reflection of light incidence is equal to angle of reflection.1st Law:The angle of incidence is equal to angel of reflection.i.e. Li = Lr2nd Law: The incident ray, the reflected ray and the normal all lie in the same plane.Regular and Irregular Reflection: When rays of light fall on a smooth and shinning surface, like a plane mirror, most of them are reflected in a particular direction. Such a reflection is called regular reflection or specular reflection. Such a reflection is used in construction of images. When rays of light fall on a rough surface, like a white paper or a painted wall, the rays are reflected back in different directions. Due to the roughness of the surface, the angle of incidence is different for different rays, therefore the reflected rays scatter in different directions. Such a reflection is called irregular reflection or diffuse reflection.Irregular reflection is very important for us. We receive light at dawn or after sunset, due to the irregular reflection of sunlight from dust particles in air. All the nonluminous objects are visible due to irregular reflection of light from their surfaces.Image formed by a Plane Mirror:Two rays starting from the object after reflection from the mirror appear to meet at the image. Thus to the eye, virtual image of the object will be seen behind the mirror.A ray from O falling normally on the mirror is reflected back normally and another ray falling at a certain angle of incidence is reflected back at the same angle of reflection (according to law of reflection Li = Lr). The two reflected rays appear to meet at I. hence I is the virtual image of the object O.The two triangles are congruent; therefore, the distance of image I from the mirror is equal to the distance of the object O from the mirror. The characteristics of image formed by a plane mirror are given follows:(1) Images are laterally inverted. That is the right side of the object

appears as the left side of the image.(2) Images are of the same size as objects.(3) Images are virtual and can not be obtained on the screen.(4) Image is at the same distance from mirror as the object. Spherical Mirrors:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Spherical Mirrors is a section of a hollow sphere. If the inner surface is polished, then it is called a converging or concave mirror. If the outer surface of the spherical mirror is polished then it is called a diverging or convex mirror.Let us study certain terms used in spherical mirrors.a) Centre of curvature (C): The centre of the sphere is called centre of curvature of the mirror.b) Radius of curvature (R): The radius of sphere is called radius of curvature of mirror.c) Principal axis: The line passing through pole and centre of curvature of mirror is called principal axis.

Mirror Formula (Equation for Spherical Mirror):If p be the distance of the object from the pole of the mirrorq be the distance of the image from the pole of the mirror, and f be the focal length of the mirror, then a Simple equation between them, is called mirror formulaConsider in which the A'B' of the object AB is formed by a concave mirror,Ray AP is reflected back at the same angel which it is incident obeying the law of reflection. Two triangles ABP and A'B'P are similar, thereforeAB / A'B' = PB / PB'AB /A'B' = p/q (1)Again two triangles ABF and PDF are similar. Therefore AB / PD = BF / PF Since PD = A'B', and BF = (p-f)We have AB / A'B' =(p-f)/f (2) Left hand side (L.H.S) of equations (1) and (2) are equal equalEquation their right hand sides (R.H.S), we get. p/q = (p-f)/f Dividing both sides by p, we get p / qp = p- f / pf p / qp = p / pf – f / pf or 1/q= 1/f – 1/p or 1/f = 1/p + 1/q



CHAPTER NO 14 REFRACTION OF LIGHT AND OPTICAL INSTRUMENTS

Topics of the Chapter:(a)Refraction of Light(b)Refraction of Light through a Prism (c) Lenses (d)Thin Lens Formula (e) Optical Instruments

Refraction of Light:"The change in direction and velocity of light as it enters from a medium into another, is called refraction of light."The refraction of light is explained in which the boundary AB separates the two media. CO is called incident ray, OE is called refracted ray, point O is called point of incidence, NON' which is perpendicular to AB is called normal, LCON = Li is called angle of incidence, and LN'OE = Lr is called angle of refraction.Refraction of light obeys two laws, called the laws of refraction.


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= 1st law:"The incident ray, the refracted ray and the normal to the surface at the point of incidence, lie in the same plane".2nd law:"The ratio of sine of angle of incidence (Sin i) to the sine of angle of refraction (Sin r) remains constant for the two media."This constant is called refractive index and is denoted by n.Hence n = Sin i /Sin rit may be noted that (1) When light enters from rarer to denser medium, it bends towards the normal.And (2) When light enters from denser to rarer medium, it bends away from the normal.The 2nd law of refraction is also called Snell's Law. It may be noted that if a ray of light enters normally into the other medium, there is no change in direction. The refractive index of a medium is also defined as "The ration of speed light in vacuum or air to the speed of light in the medium."Hence Refractive index = Speed of light in air_______ Speed of light in the medium Refraction of light through a Prism:A prism is transparent body having three rectangular and two triangular surfaces. The angle opposite to the base of its triangular, face is known as angle of the prism. The path of ray EF as it is refracted from a prism. OL is normal to AB and PQ is normal to AC. When ray EF enters the prism. It bends towards the normal OL and when it comes out from the prism, it bends away from the normal PQ. EF is called the incident ray. FG is called refracted ray. GH is called the emergent ray.LEFG = Li is called the angle of incidence, and LLFG = Lr is called the angle of refraction. If the incident rays EF and the emergent ray HG are produced, they meet at M.LHMK = LD is called angle of deviation.The angle of deviation D depends upon the angle of incidence i. At some of incidence, D has minimum value. This minimum value is called angle of minimum deviation and is written as Dm. In this position the refracted ray FG is always parallel to the base BC. If A be the angle of the prism, and Dm be the angle of minimum deviation, then the refractive index of the material of the prism is found to be


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= Sin (A+Dm) 2n = _____________________ Sin A 2

Lenses:Lenses are made up of transparent refraction of medium (glass or plastic) bounded by one or two spherical surfaces. The lenses are of two types, (1) the convex, and (2) the concave lens.(1)Convex Lenses: The thickness of the convex lens at the middle is greater than at as edges. A convex lens converges a parallel beam of light to a point, therefore it is also called converging lens. There are three types of convex lenses

(1)Double convex lenses: Both the surface of a double convex lens is convex.

(2)Plano convex lenses: One surface is convex and the order is plane (3)Concavo convex lenses: One surface is convex and the other is

concave.(2)Concave lenses: A concave lens is thinner at the middle and thicker at the edges. A concave lens diverges a parallel. They are also of three types.a) The double concave lens b) The Plano concave lens and c) convexo-concave lens

Thin lens Formula:The nature and the position of image can be found by using the following formula, called the lens formula.1/p +1/q = 1/f Here P is the distance of the object from the lens Q is the distance of the image from the lens, and F is the focal length of the lens.Following sign convention is used while applying lens formula.

(1)All distances are measured from the optical centre of the lens.(2)Distance of the real objects and real images are taken positive and

the distances of virtual objects and virtual images are taken negative.

(3)The focal length of convex lens is taken positive and the focal length of concave lens is taken negative lens has virtual focal point.

Optical Instruments:(1) Camera:


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= It is an optical instruments by which permanent image of an object is obtained on a sensitive screen. It consists of a light proof container blackened inside to absorb stray light. In ordinary camera, a convex lens is situated at the front but in costly camera a combination of lenses is used. The purpose of the real and inverted image of the object is on the sensitive screen situated at the back of the camera. The lens of the camera can be moved in or our out with the help of mechanical mount in order to get sharp image.There is a shutter between the film and the lens. When a photograph is taken, the shutter opens for a very short time on the sensitive screen or photograph film. The formation of a clear and well focused image in a camera depends upon the following factors.

(1) Diameter of the aperture of Camera: It adjusts the amount of light entering the camera.

(2) Focal length of the lens: It adjusts the area and size of the image.(3) The time for the opening of shutter: It is so adjusted that the film

is exposed to the light properly and clear and distinct image is formed on the film.

Compound Microscope: The compound microscope is used when ever high magnification is required. The magnifying power of a simple microscope can be increased

by decreasing the focal length of the lens as M = But due to

constructional difficulties, the focal length of the lens can’t be decreased beyond a certain limit. Therefore to increase the magnifying power, two separate lenses are used. The lens near the object is called the OBJECTIVE and the other which is nearer the eye is known as thee EYE PIECE. The objective and eye piece are both convex lenses, The objective is of small diameter and small focal length (high power) when

the eye piece is of large focal length then the objective.The AB is placed at a distance slightly greater than the focal length of the objective. An inverted image A’ B’ is formed of A’. The eye piece is adjusted so that the distance of A’ from it is less than its focal length. As the eye piece acts as a simple magnifying glass, the final image PQ is

formed at P which magnified and virtual.


Fo

F A’B O

Q

P

B

d

Eye Piece

Eye

(Compound microscope)

Fin

al I

mag

e


CHAPTER NO 16 ELECTRICITY

Topics of the Chapter:(a)Coulomb's Law (b)Electric Field(c) Capacitor(d)Electric current(e) Resistance(f) Ohm' law

Coulomb's Law: Introduction: This first experiment to study the force between two point charges was carried out by Coulomb in 1785 by means of an apparatus called torsion balance. The results of his observations are stated in a law, called Coulomb's Law.Statement: "The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distances between them"Explanation: If q 1 and q 2 be the point charges at a distance r from each other placed in vacuum or air as shown in the given figure, then according to the above statement, the magnitude of the force F is given as: F œ q 1 q 2 → (1) F œ 1


FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= r2 → (2) By comparing both eq: then we get F œ q 1q 2

r2 or → (1) When K is a constant and its value depends upon the system of kinds

used and the medium between the charges. The unit of charge in S.I system is Coulomb. It is depend in terms of

electric current which is a fundamental quantity having unit Ampere. One Coulomb charge is that quantity of charge which crosses any part

of the wire in one second when a constant current of 1ampere flows through it

In equation (1), if q 1 = 1 coul. q 2 = 1 coul. And r = 1 m and of the charges are placed in vacuum, then F = 9×109 N By using there values in equation (1) then we get 9×109 N = K 1coul × 1coul 1 m2 9×10 9 N× 1m 2 = K 1 coul × 1 coul Or → (2)

In the vector form, equation (1) can be written as → (3)

Where F12 means force of q 1 ε▫ q 2

and r 12 is unit vector along r having direction from q 1 towards q 2

In advanced electricity, another constant ε▫ called permittivity of free space is used. It is supposed as ε▫ = 1__ = 1________ = 8.85×10 – 12

4πk 4×3.14×9×109 Thus → (4)

From this supposition we leave


F = K q1 q 2 r2

K = 9× 109Nm2/coul2

F12 = K q1 q2 r12

r2

ε▫ = 8.85 × 10 – 12 coul 2/Nm2

FAMCY Educational institute of computer English Language and coaching center Created by Dr Asif Rattar ============================================================= K = 1__ 4π ε▫ Using it in equation (1), we get → (5) Electric current:When charges move in a wire an electric current is said to flow through the wire. The electric current through a conductor is defined as the amount of charge passing through any part of the conductor per second. It is denoted by I.

If Q charges passes through a conductor in t sec then current I is given by

UNIT:The unit of current is AMPERE (A).The current is said o be one

‘ampere” When one coulomb of charge passes through any part of the wire in one second.i.e.

1 ampere =

The smaller units are as given below.I micro ampere (1 A) = 10-6 AI milli ampere (1mA) = 10-3 A

Resistance:

COMBINATION OF RESSITORWe often encounter circuits where resistors are connected in series

or in parallel. In both cases, the total current flow from the battery and its power output can be calculated if the equivalent resistance is determined.1. SERIES COMBINATION:

A number of resistors R1, R2, and R3 are said to be connected in series if they are connected end to end connectivity that the same current I flows through ach.


F = 1_ q 1 q 2

4π ε▫ r2

+V

R1 R2 R3


If in place of the above three resistance only one resistance Re is joined to the battery the resistance Re is called the equivalent resistance.

By Ohm’s LawV = IRe

If V1, V2 and V3 be the potential difference across R1, R2 and R3, then V= V1 + V2 + V3

But V1=IR1, V2= IR2, V3= IR3 IRe = IR1+ IR2 + IR3

Re = R1 + R2 + R3

If there are more than three resistors in series, then a single equivalent resistance can be given as

II. PARALLEL COMBINATION:When the resistors are combined between two common terminals

then such a combination is called parallel combination. Consider three resistors R1, R2 and R3 are connected in parallel as shown in fig.


Re

+V

V

R3

R2

R1

+ –

V


We will suppose that main current I divides into I1, I2 Into I1, I2 and I3 through the resistors R1, R2 and R3 rep. And that the common p.d across then is V. if RIs the equivalent resistance then.

and I = I1 + I2 + I3

Where I1 = V/R1, I2 = V/R2 + V/R3

for more than three resistors

Ohm's Law:According to ohm’s (German Scientist George Ohm), “The current

through a conductor is directly proportional to the potential difference between the ends of the conductor, provided that physical conditions remain the same.” The physical state of the conductor means nature of material, temperature and dimension of t he conductor.

Consider a conductor ab through which an electric current I flows, when a potential difference V is applied across it.

By Oh’s Law V I

OR V=IR 1This is the mathematical from of Ohm’s law. Where R is constant

of proportionality called as ‘resistance” of the conductor and depends upon the nature, dimension and temperature of the conductor. From equation 1.

and

The S.I unit of resistance is the Ohm, shown as (The Greek letter Omega).The resistance of the conductor is said to be one Ohms if a current of one ampere passes through it when a P.d of 1 volt is applied across its end.


I

+ –



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Physics Notes For Tenth Class by Muhammad Arif Rattar

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