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CLASS IX & X
PHYSICS
FORMULA SHEETS
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CLASS – IX
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CHAPTER – 1: MOTION
Speed and Velocity
distance travelledSpeed
time taken
sv
t
displacement Velocity
time
sv
t
Acceleration
change in velocity
Accelerationtime taken
v ua
t
Unit of acceleration = ms2, cm/s2, km/h2
Equations of Uniformly Accelerated Motion
(a) 1st Equation of Motion:
v = u + at …..(i)
(b) 2nd Equation of Motion:
21
2s ut at … (ii)
(c) 3rd Equation of Motion:
2as = v2 – u2 or v2 = u2 + 2as ….(iv)
Motion Under Gravity (Uniform Accelerated Motion)
(i) If a body moves upwards (or thrown up) ‘g’ is taken negative (i.e. motion is against gravitation
of earth). So we can form the equation of motion like,
v = u – gt, s = ut 1
2 gt2, v2 – u2 = – 2gh.
(ii) If a body travels downwards (towards earth) then ‘g’ is taken positive. So equations of motion
becomes
v = u + gt, s = ut + 1
2gt2, v2 – u2 = 2gh.
(iii) If a body is projected vertically upwards with certain velocity then it returns to the same point
of projection with the same velocity in the opposite direction.
(iv) The time for upward motion is the same as for the downward motion.
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Angular Displacement and Angular Velocity
;Angular displacement
Angular velocityTime taken t
t
Relation between Linear Velocity and Angular Velocity
v r
Linear Velocity = radius × Angular velocity
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CHAPTER – 2: FORCE
Force
A force is an external agency that displaces or tends to displace a body from its position of rest. The
direction in which the object is pushed or pulled is called the direction of the force. Force has both
magnitude and direction. It is a vector quantity.
“Force is the cause which can produce acceleration in the body on which it acts”.
Effects of Force:
The force or a set of forces acting on a body can do three things:
(i) A force or a set of forces can change the speed of the body.
(ii) A force or a set of forces can change the direction of motion.
(iii) A force can change the shape of the body.
Units of Force
(a) In C.G.S. System:
∴ F = ma → gm × cm/s2 = Dyne
(b) In S.I. System:
F = ma → kg × m/s2 = Newton
Linear Momentum: p mv
Newton’s first law : Inertial frame.
Newton’s second law: ,dp
Fdt
F ma
Newton’s third law: AB BAF F
Frictional force: fstatic, max = μsN, fkinetic = μkN
Banking angle: 2 2 tan
tan ,1 tan
v v
rg rg
Centripetal force: 2
,c
mvF
r
2
c
va
r
Pseudo force: 0 ,pseudoF ma 2
centrifugal
mvF
r
Minimum speed to complete vertical circle
min, bottom 5 ,v gl min, topv gl
Conical Pendulum: cos
2l
Tg
mg
T
l
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Conservation of Linear Momentum Formula
The principle of conservation of momentum states that if two objects collide, then the total momentum
before and after the collision will be the same if there is no external force acting on the colliding
objects.
Initial momentum = Final momentum
i fP P
Angular Momentum Formula
Angular momentum can be experienced by an object in two situations. They are:
Point object:
The object accelerating around a fixed point. For example, Earth revolving around the sun. Here the
angular momentum is given by:
L r p
Where,
L is the angular velocity
R is the radius (distance between the object and the fixed point about which it revolves)
p is the linear momentum.
Extended object
The object, which is rotating about a fixed point. For example, Earth rotates about its axis. Here the
angular momentum is given by:
L I
Where,
L is the angular momentum.
I is the rotational inertia.
is the angular velocity.
Impulses of Force
Impulse = Force × Time
or I = F. t
The S.I. unit of impulse is Newton-second (N-s) and the C.G.S unit is dyne - second (dyne -s).
Impulse and Momentum:
From Newton’s second law of motion
Force, 2 1p pF
t
or 2 1.F t p p
i.e., Impulse = Change in momentum
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CHAPTER – 3: GRAVITATION
1. Newton’s Universal Law of Gravitation
F = 2
1 2 G m m
d
2. Unit of Gravitational Constant:
G = 2
1 2
Fd
m m
SI unit of G = 2
Nm
kg kg=
2
2
Nm
kg= Nm2 kg–2
CGS unit of G is dyne cm2 g-2
The value of G = 6.67 × 10-11 N m2 kg-2 or 6.67 × 10-8 dyne cm2 g-2
= The value of G was found by Henry Cavendish.
3. Gravitational acceleration: 2
GMg
R
4. Variation of g with depth: inside
1 hg g
R
5. Variation of g with height: outside
1 2hg g
R
6. Effect of non-spherical earth shape on g
g at pole > g at the equator (since Re – Rp ≈ 21 km)
7. Orbital velocity of the satellite: 0
GMV
R
8. Relation between Escape Velocity and Orbital Velocity
02eV V
9. Kepler’s Law
First Law: Eliptical orbit with the sun at one of the focus.
Second Law: Areal velocity is constant 0dA
dt
Third Law: 2 3T R
10. LAW OF FLOATATION
Weight of the floating solid = weight of the liquid displaced.
i.e. 1 21 1 2 2
2 1
VV g V g
V
or Density of solid Volumeof theimmersed portionof the solid
Density of liquid Total volumeof the solid
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CHAPTER – 4: WORK POWER & ENERGY
WORK, POWER AND ENERGY
Work:
. cos ,W F S FS .W F dS
Kinetic energy: 2
21
2 2
pK mv
m
Potential energy:
/F U x for conservative forces.
gravitational ,U mgh 2
spring
1
2U kx
Work done by conservative forces is path independent and depends only on initial and final points:
conservative. 0.F dr
Work-energy theorem: W K
Mechanical energy: E = U + K. Conserved if forces are conservative in nature.
Power: ,av
WP
t
instP F v
Some manmade devices which convert one form of energy into another are given as follows.
DEVICE INPUT ENERGY OUTPUT ENERGY
1. Fan Electrical energy Kinetic energy
2. Electric lamp Electrical energy Light energy
3. Electrical heaters Electrical energy Heat energy
4. Radio Electrical energy Sound energy
5. Water pump Electrical energy to kinetic energy of impeller
to potential energy of water
6. Cell Chemical energy Electrical energy
7. Microphone Sound energy Electrical energy
8. Rechargeable cell (a) During discharging
Chemical energy
(b) During charging
Electrical energy
(a) Electrical energy
(b) Chemical energy
9. Loudspeaker Electrical energy Sound energy
10. Elevator moving up Electrical energy Potential energy
11. Television Electrical energy Sound energy, light energy
12. Thermal power plant Chemical energy of coal Electrical energy
13. Car Chemical energy of
petrol/diesel
Mechanical energy
14. Nuclear power plant Nuclear energy Electrical energy
15. Solar cell Solar energy Electrical energy
16. Watch Potential energy of
wounded spring
K.E. of hands or watch
17. Generator Kinetic energy Electrical energy
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CHAPTER – 5: SOUND
SOUND
Sound is mechanical energy, which produces sensation of heating.
Sound is produced due to vibration of different objects.
A material medium is essential for the propagation of sound as it cannot travel in vacuum.
A region of compressed air (increased density of pressure) is called a compression and that of
rarefied air (decreased density or pressure) is called a rarefaction.
LONGITUDINAL AND TRANSVERSE WAVES
A wave motion is a form of disturbance (a mode of momentum and energy transfer) which is
due to repeated vibrations of the particles about their mean positions and the motion is
transferred from one particle to the other without any net movement of the medium. A wave
motion is of two types:
(i) Longitudinal (ii) Transverse
Sound waves are longitudinal waves. Light waves, on the other hand, are transverse waves.
Sound wave propagates as compressions and rarefactions. (i.e., as variation in density of
pressure) in the medium.
As sound propagates, it is the sound energy that travels in the medium and not the medium
itself.
The change in density (or pressure) from the maximum value to the minimum value and again
to the maximum value is called an oscillation.
The number of complete oscillations per second is called the frequency (v) of the sound wave.
The unit of frequency is called hertz (Hz).
The time taken for one complete oscillation in density (or pressure) of the medium is called the
time period (T) of the wave.
The distance between two consecutive compressions (or crests) or two consecutive rarefactions
(or troughs) is called the wavelength. The unit of wavelength is meter (m).
The distance travelled by a sound wave in its periodic time is also called wavelength (λ) of the
wave.
The relation between frequency (v) and time period (T) is 1 1
,v TT V
or v T = 1.
The speed of sound depends mainly on its nature and the temperature of the medium through
which its propagates.
The relation between speed of the sound wave (v), its frequency (v) and wavelength (λ) is v = vλ.
The sound wave is described by: (i) Its speed, (ii) Its frequency (or wavelength) and
(iii) Its amplitude.
In general, speed of sound in solids > speed of sound in liquids > speed of sound in gases.
However, this relation is not always valid.
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Sources that move faster than the speed of sound are said to have supersonic speeds. Bullets,
jet aircrafts etc. travel at supersonic speeds.
A shock wave is produced when sound producing source moves with a speed higher than the
speed of sound.
It is not necessary for an object to be a vibrating source of sound to produce a shock wave.
A shock wave carries a large amount of energy.
Sonic boom is a very sharp and loud sound produced by pressure variation associated with a
shock wave.
ECHO
Like light waves, sound waves are also reflected from a surface on which they fall. The laws of
reflection of sound are the same as those of light.
The echo is the phenomenon of repetition of sound of a source by reflection from an obstacle.
The time interval between the incident sound and the reflected sound for hearing a distinct
echo is 0.1 s and this property is called persistence of hearing.
For hearing a distinct echo the minimum distance of the obstacle from the source of sound
should be 17.2 m. This distance changes with change of temperature.
MULTIPLE ECHO
Multiple echoes are heard when sound is repeatedly reflected from a number of obstacles at
suitable distances.
REVERBERATION
Reverberation is the phenomenon of persistence or prolongation of audible sound after the
source has stopped emitting sound.
Reverberation is reduced by (i) carpeting the floor (ii) upholstering furniture and (iii) creating
false ceilings with a suitable sound absorbing material.
The ceilings of concert halls are curved to enable the sound in reaching all corners of the hall.
A sound board is used to evenly spread the sound throughout the width of the hall.
The audible range of hearing for average human beings is in the frequency range of 20 Hz to
20kHz. Children under the age of five can hear upto 25 kHz whereas aged people become less
sensitive to higher frequencies.
INFRASOUND AND ULTRASOUND
Infrasound (or infrasonic) has a frequency below 20 Hz.
Ultrasound (or ultrasonic) has a frequency above 20 kHz.
APPLICATIONS OF ULTRASOUND
(i) Industry (ii) Medical Science
(iii) Communication (iv) SONAR
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In industry, ultrasound is used in:
(i) Cleaning instruments and electronic equipments
(ii) Plastic welding
(iii) Detecting flaws and cracks in metal blocks used in constructing big structures.
In medical science, ultrasound is used in:
(i) Echo-cardiography (ii) Ultrasonography
(iii) Surgery (iv) The rapeutics.
SONAR is Sound Navigation and Ranging and is used to measure distance, direction and
speed of objects lying under sea. It is also used in ship-to-ship communication.
HUMAN EAR
The human ear can be divided into three parts:
(i) The outer ear which collects sound waves
(ii) The middle ear which amplifies the sound waves about 60 times and
(iii) The inner ear which converts the amplified sound energy into electrical energy and
conveys to the brain as nerve impulses for interpretation.
DISTANCE BETWEEN THE SOURCE OF SOUND AND OBSTACLE:
Let the distance between observer and the obstacle = d
Speed of sound (in the medium) = v
Time after which echo is heard = t
Then, t = 2 v
v 2
d tor d
The minimum distance (in air at 25oC) between the observer and the obstacle for the echo to be heard
clearly should be 17.2m.
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CLASS - X
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CHAPTER – 1: ELECTRICITY
ELECTRICITY AND ITS EFFECT (NOTATIONS)
Physical Quantity Symbols SI Unit
Voltage (potential difference) V Volt (V)
Power P Watt (W)
Charge Q Coulomb (C)
Work or Energy W Joule (J)
Resistance R Ohm (Ω)
Current I Ampere (A)
Resistivity ρ Ohm metre (Ω m)
CURRENT
The rate of flow of charges (Q) through a conductor is called current (I) and is given by.
ChargeCurrent = or I= .
Time
Q
t The SI unit of current is ampere (A).
1 coulomb1 Ampere =
1 second
ELECTROMOTIVE FORCE
The potential difference at the terminals off cells in an open circuit is called electromotive force (emf)
and is denoted by letter E.
Potential difference is the work done in bringing a unit charge from one place to another.
WorkPotential Difference = ,
Charge
1 Joule1 Volt
1 Coulomb
JV
C
OHMS LAW
AT any constant temperature the current (I) flowing through a conductor is directly proportional to the
potential difference (V) across it. Mathematically.
I ∝ V vice-versa V ∝ I
or V = RI ,V V
R II R
Where R – Resistance, V – Voltage (P. D.), I – Current
SYMBOLS OF A FEW COMMMONLY USED COMPONENTS IN CIRCUIT DIAGRAM
Component Symbol Component Symbol
An electric cell Electric Bulb
Battery of Cells
A resistance
Plug key or switch (open) or
Variable
Resistance
(Rheostat) or
l
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A closed plug or switch or
Ammeter A+ –
A wire joint
Voltmeter V+ –
RESISTANCE
Resistance is a property of a conductor by virtue of which it opposes the flow of electricity through it.
Resistance is measured in Ohms (Ω). Resistance is a scalar quantity.
CONDUCTOR
Low-resistance material which allows the flow of electric current through it is called a conductor. All
metals are conductors except Hg and Pb etc.
RESISTOR
High-resistance materials are called resistors. Resistors become hot when current flows through them
(nichrome wire is a typical resistor).
INSULATOR
A material which does not allow heat and electricity to pass through it is called an insulator. Rubber,
dry wood etc., are insulators.
IMPORTANT FORMULAE:
1. Coulomb’s Law
1 2
2
k q qF
r
(k is constant of proportionally)
q1 and q2 = two electric changes
r = distance between two electric charges
F = Force
2. ; ;W W
V W V Q QQ V
V = p.d., W = Work done, Q = Quantity of charge transferred
3. ; ;V V
V R I R II R
V = p.d., R = Resistance, I = Current
4. ;l R A
RA l
R = Resistance; l = length, A = Area of cross section; ρ = rho, a constant known as resistivity.
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5. Series combination R = R1 + R2 + R3 …. + Rn
6. Parallel combination 1 2 3
1 1 1 1....
nR R R R R
For equal resistances
Rs = nR (For series connection)
R
Rpn
(For parallel connection)
2Rsn
Rp
Rs = Effective resistance in series
Rp = Effective resistance in parallel
n = number of resistors
R = Resistance of each resistor
7. Work Energy consumed
; Power = Time Time
WP
t
8. ;W V I t Power = potential difference × current × time
2
2 V tW I Rt W
R
9. P = V × I; Power = potential difference × current
10. P = I2 × R; Power = (current)2 × resistance
11.
22 potential difference; Power =
resistance
VP
R
12. Electric energy = P × t; electric energy = power × time
13. Heating Effects of Current: H = I2Rt
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CHAPTER – 2: LIGHT
LAW OF REFLECTION
1. Incident ray, reflected ray and normal at the point of
incidence lie in the same plane.
2. The angle of incidence is equal to the angle of
reflection i.e., ∠i = ∠r.
REFLECTION FROM A PLANE MIRROR
1. The image is virtual. The image and the object are
equidistant from the mirror.
2. The object size is equal to the image size i.e.,
magnification is 1.
REFLECTION FROM A SPERICAL MIRROR
1. Focal length is equal to half of radius of curvature i.e., f = R/2.
2. The object distance u, image distance v and focal length f are related by the mirror formula:
1 1 1
v u f
3. The magnification is the ratio of image height to the object height and it is given by
v
mu
IMAGE FORMATION FROM CONCAVE MIRROR
S.
No.
Position of
the object
Position of
the image
Nature & size of
the image Ray diagram
(
1) At infinity At focus F
Real, inverted
and highly
diminished.
(point size)
(
2)
Between
infinity
and C
Between C
& F
Real, inverted
and smaller than
the object
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(
3) At C At C
Real, inverted
and same size.
(
4)
Between
C & F
Between C
and infinite
Real, inverted
and enlarged.
(
5) At F At infinity
Real, inverted
and infinitely
large.
(
6)
Between
focus
and pole
Behind the
mirror
Virtual, erect and
enlarged.
IMAGE FROM A CONVEX MIRROR
S. No. Position of the
object
Position of the
image Size of image
Nature of the
image
(i) At infinity At F, behind mirror Highly diminished Virtual and erect.
(ii) Between infinity
and pole of mirror
Between P & F
behind the mirror
Smaller than object Virtual and erect.
SIGN CONVENTION OF SPHERICAL MIRROR
(i) Whenever and wherever possible, the ray of light is taken to travel from left to right.
(ii) The distances above principal axis are taken to be positive while below it, negative.
(iii) Along principal axis, distances are measured from the pole and in the direction of light are taken
to be positive while opposite to it is negative.
FORMULAS ON REFRACTION OF LIGHT
Refractive Index
speed of light in vacuum c
speed of light in medium v
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Laws of Refraction
1. Incident ray, refracted ray and normal at the point of incidence lie in the same plane.
2. The angle of incidence is related to the angle of refraction by Snell’s Law:
2
1
sin
sin
i
r
Lens Formula
The object distance u, image distance v and focal length f of a lens are related by the lens formula
1 1 1
v u f
The magnification by a lens is given by
vm
u
Power of a Lens
The power of a lens is related to its focal length by
P = 1/f
The power P in diopter if f in metre.
For Convergent or Convex Lens
S. No. Object Image Magnification
1 At At F m << - 1
2 - 2F F – 2F m < - 1
3 2F At 2F m = - 1
4 At F – 2F - 2F m > - 1
5 At F At m >> -1
6 F – O In front of lens m > + 1
Combinations of Lenses
If two thin lens are placed in contact to each other then,
power of combination, P = P1 + P2
1 2
1 1 1
F f f
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CHAPTER – 3: MAGNETIC EFFECTS OF ELECTRIC CURRENT
1. Magnetic field due to a moving point charge:
0
34
q v rB
r
7 2 2
0 4 10 /N s C is called the permeability of free space.
2. Biot-savart’s Law:
This law states that tahe magnetic field (dB) at point P due to small current element Idl of the
current-carrying conductor is directly proportional to the Idl (current) element of the conductor
2
. . sinI dldB
r
3. Magnetic field due to a straight wire
I r
P
01 2sin sin
4
IB
r
4. Magnetic field due to an infinite straight line
rP
0 1
2B
r
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5. Magnetic field due to a circular loop
r
I
(i) At centre
B = μ0NI/2r
(ii) At axis
2
0
32 2 2
2
NIRB
R x
6. Magnetic field on the axis of a solenoid
B = (μ0NI/2) (cosθ1 – cosθ2)
7. Amperes Law
0.B d I
8. Magnetic field due to a long cylinder
(i) B = 0, r < R (ii) 0 ,2
IB r R
r
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9. Magnetic force acting on a moving point charge
r
B
V
F q v B
10. Magnetic force acting on a current-carrying wire
F I B
11. Magnetic Moment of a current carrying loop
M NIA
12. The torque acting on a loop
M B
13. Magnetic field due to single pole
0
22
mB
r
14. Magnetic field on the axis of the magnet
0
3
2
4
MB
r
15. Magnetic field on the equatorial axis of the magnet
0
34
MB
r
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CHAPTER – 4: THE HUMAN EYE & COLOURFUL WORLD
REFRACTION BY A PRISM
The incident ray suffers a deviation (or bending) through an angle due to refraction through the
prism. The angle is called the angle of deviation.
Note:
1. The prism is in the position of the minimum deviation when angle of emergence e = angle
of incidence i .
2. The refractive index of the material of prism is given as
mAsin
2
Asin
2
DISPERSION OF WHITE LIGHT BY A GLASS PRISM
Dispersion of light
The process of splitting of white light into its
seven constituent colours is called dispersion of
white light. The band of seven colours formed on
a screen due to the dispersion of white light is
called spectrum of visible light or spectrum of
white light.
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CHAPTER – 5: SOURCES OF ENERGY
NUCLEAR FISSION
Nuclear fission reaction is that in which a heavier nucleus breaks down into two or more
lighter nuclei of nearly equal size (mass) with the release of large amount of energy.
235 1 143 90 1
92 0 56 36 03 200 .U n Ba Kr n MeV
The above nuclear fission reaction was first observed by Hahn and strassman.
NUCLEAR FUSSION
The fusion of two lighter nuclei in a stable heavier nucleus with the release of large amount of
energy is called nuclear fusion.
1 4 0
1 2 14 2 27H He e MeV
UNIT OF RADIOACTIVITY
The SI unit for activity is becquerel, Henry Becquerel .Becquerel is simply equal to 1 disintegration or
decay per second. There is also another unit named “curie” that is widely used and is related to the SI
unit as:
1 curie = 1 Ci = 3.7 × 1010decays per second= 3.7 × 1010Bq
TYPES OF RADIOACTIVE DECAY
Alpha decay: An alpha particle (A = 4, Z = 2) is emitted from the nucleus, resulting in a
daughter nucleus (A -4, Z - 2).
Proton emission: The parent nucleus emits a proton, resulting in a daughter nucleus (A -1, Z - 1).
Neutron emission: The parent nucleus ejects a neutron, resulting in a daughter nucleus (A - 1, Z).
Spontaneous fission: An unstable nucleus disintegrates into two or more small nuclei.
Beta minus (β−) decay: A nucleus emits an electron and electron antineutrino to yield a
daughter with (A, Z + 1).
Beta plus (β+) decay: A nucleus emits a positron and electron neutrino to yield a daughter with
(A, Z – 1).
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Number of particles emitted Mass number difference
4
Number of particles emitted
2 Atomic number difference
Number of particles 4
b d
Number of particles ( )
2
b dc a
HALF-LIFE
The term half-life was introduced by Rutherford.
The time required to decay exactly one half of the initial amount of a radioactive element is
called half-life of that element 1 0.5 50%
2
or or .T T T
1
2
0.693
decay constantT