physics-ALMC

MC Question

Chapter 18 Gases (MC)18P1

1. (80)

A mixture of two gases X and Y is maintained at constant temperature. The relative molecular mass of X is 9 times

that of Y. What is the ratio of the r.m.s. speed of molecules of Y to that of molecules of X?

A. 3 B. 3 2 C. 9 D. 18 E. 81

2. (81)

The equation of state for mass m of an ideal gas may be written as p V = m r T. With reference to this equation,

(1) the value of r depends upon the particular gas used.

(2) r is independent of m.

(3) if R is the universal gas constant, then the mass of each mole of this gas is R / r.

A. (1) only B. (3) only C. (1) & (2)only D. (2) & (3) only E. (1), (2) & (3)

3. (81)

An ideal gas is enclosed in a container at absolute temperature T. The absolute temperature is now raised to 2T,

whilst the volume is kept constant. Which of the following statements is correct ?

(1) The average separation of the molecules is reduced by a factor of 2 .

(2) The average speed of the molecules is doubled.

(3) The average kinetic energy of the molecules is doubled.

A. (1) only B. (3) only C. (1)&(2)only D. (2)&(3)only E. (1),(2)&(3)

4. (82)

Mass M of an ideal gas at pressure p occupies volume V. The r.ms. speed of its molecules is

A. MpV 3/

B. MpV /

C. MpV /3

D. pVM

E. pVM3

5. (83)

A cylinder containing air is fitted with an air-tight frictionless piston maintained at a constant temperature. The

piston is moved very slowly inwards until the volume of the cylinder has halved, Which of the following

quantities has doubled ?

(1) The average speed of the gas molecules in the cylinder.

(2) The average momentum of the gas molecules in the cylinder.

(3) The average force exerted by the gas molecules on the piston.

A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only E. (l), (2) & (3)

6. (84)

A fixed mass of gas at s.t.p. occupies a volume of 1 m3. The gas is heated and allowed to expand to a final volume

of 2 m3 with its pressure doubled. The average kinetic energy of the gas molecules is

A. reduced to one quarter of its initial value.

B. halved.

C. unchanged.

D. doubled.

E. increased four times.

MC Question


N

vc

P

T

P

T

A BS

1

1

2

2

N 2 N

container X container Y

7. (84)

The graph shows the distribution of speeds (v) of the molecules in a constant mass of gas. Which of the following

statements is/are correct?

(1) The value v = c at which the peak of the curve occurs increases when the temperature rises.

(2) The peak of the curve rises when the temperature rises.

(3) Provided that the temperature does not change, the kinetic energy of each molecule is fixed.

A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only E. (1), (2) & (3)

8. (85)

According to the kinetic theory of gases, at a given temperature, the molecules of different gases have the same

(1) average speed.

(2) average kinetic energy.

(3) average total energy

A. (1) only B. (3) only C. (I) & (2) only D. (2) & (3) only E. (1), (2) & (3)

9. (85)

A vessel of volume 1 u 10-3 m3 contains 0.72 g of an ideal gas at a pressure of 1 u 105 Pa. The r.m.s. velocity of the gas molecules is

A. 20 m s-1 B. 110 m s-1 C. 340 m s-1 D. 650 m s-1 E. 3400 m s-1

10. (85)

A and B are two identical containers connected by a tap S initially closed. A contains an ideal gas at a pressure P1

and a temperature T1. B contains the same gas at a pressure P2 and a temperature T2. The tap S is then opened. If

the temperatures of the containers A and B remain constant at T1 and T2 respectively, the final pressure of the gas

mixture will be

A. (P1 + P2) / 2.

B. (P1 + P2).

C. (P1T1 + P2T2) / (T1 + T2).

D. (P1T2 + P2T1) / (T1 + T2).

E. (P1T1 + P2T2) u (T1 + T2).

11. (86)

Container X holds N molecules of a certain gas at atmospheric pressure. Container Y has the same volume as X

and hold 2N molecules of the same gas. Both containers are at the same temperature. The ratio of the average

number of collisions per second with the walls in X to those in Y is

A. 1 : 2 B. 1 : 2 C. 1 : 1 D. 2 : 1 E. 4 : 1

MC Question


c

N (c )

X

Y

P

/ CoT

Y

X

P

/ CoT

X, Y

P

/ CoT

X

Y

P

/ CoT

Y

X

P

/ CoT

12. (86)

At 0C temperature and 1.00 u 105 N m-2 pressure, the density of a gas is 0.179 kg m-3 . The r.m.s. speed of the gas molecules at 91C will be

A. 231 m s-1. B. 470 m s-1. C. 1290 m s-1. D. 1490 m s-1. E. 1730 m s-1.

13. (87)

The graph shows the distribution of molecular speeds c for a gas at room temperature. N (c) represents the number

of molecules 'N in a small range of speeds c to c + 'c so that 'N = N (c) 'c. As the temperature is increased,

A. the peak position will move to the right and its height will increase.

B. the peak position will move to the right and its height will decrease.

C. the peak position will move to the left and its height will increase.

D. the peak position will move to the left and its height will decrease.

E. the peak position and its height will both remain unchanged.

14. (87)

Two closed vessels X and Y contain equal masses of an ideal gas. X has a greater volume than Y. When the

temperature T changes, which of the following represents the variation of the pressure P of the gas in each vessel

with temperature T?

A. B. C. D. E.

15. (88)

An ideal gas is contained in two metal cylinders A and B connected by a tap, which is initially closed. The volume

and pressure of the gas in the cylinders are as follows:

pressure / Pa volume / m3

A 5 u105 11 u10-3 B 2 u105 4 u10-3

When the tap connecting the two cylinders is opened, what will be the final pressure in the vessel ? You may

assume that the temperature remains constant.

A. 2.4 u 105 Pa B. 3.5 u 105 Pa C. 4.2 u 105 Pa D. 5.0 u 105 Pa E. 6.9 u 105 Pa

MC Question


16. (88)

For smoke particles undergoing Brownian motion in air, the motion of the smoke particles is mainly caused by

A. air convection currents.

B. the interaction between oxygen and the nitrogen molecules.

C. collisions between air molecules.

D. collisions between smoke particles.

E. collisions between air molecules and smoke particles.

17. (88)

An inexpansible vessel contains 1.2 kg of gas at 300 K. What is the mass of gas expelled from the vessel if it is

heated from 300 K to 400 K under constant pressure ?

A. 0.25 kg

B. 0.3 kg

C. 0.6 kg

D. 0.75 kg

E. 0.9 kg

18. (88)

Which of the following is NOT an assumption in deriving the kinetic theory of gasses ?

A. The volume of the molecules is negligible compared with the volume of the gas.

B. Attractive forces between the molecules are negligible.

C. The duration of a collision is negligible compared with the time between collisions.

D. Collisions with the walls of the container and with other molecules cause no change in the average kinetic

energy of molecules.

E. The molecules suffer negligible change of momentum on collision with the walls of the container.

19. (88)

An ideal gas is at temperature T. If the mass of a gas molecule = m, the universal gas constant = R and the

Avogadro constant =NA then the r.m.s. speed of the molecules is

A. mRT /3 B. )/( AmNRT C. )/(3 AmNRT

D. mRTN A / E. mRTN A /3

20. (89)

Two vessels of equal volume both contain an ideal gas and are connected by a tube of negligible volume. Initially

both vessels are at temperature To and pressure Po. One vessel is maintained at To while the temperature of the

other is raised to T. The new pressure is then given by

A. Po B. TPo /T C. ToPo / T D. 2TPo / (T+To) E. Po(T+To)/2To

21. (89)

The internal energy of an ideal gas at temperature T is 3 C T / 2, where C is a constant.

Given that R = the universal gas constant, NA = Avogadro constant, k = Boltzmann constant.

For an ideal gas containing N molecules, the constant C is equal to

A. NAR. B. NA k. C. NR / NA. D. N k/ NA. E. NR.

22. (89)

Two different gases A and B are contained in two identical vessels. If the ratio of their molecular masses and

absolute temperatures are respectively 8 : 1 and 2 : 1, the ratio of their r.m.s. molecular speeds will be

A. 1:4 B. 1:2 C. 1:1 D.2:1 E. 4:1

MC Question


speed0

fraction ofmolecules

speed0


speed0


speed0


speed0


23. (90)

Container X holds pure hydrogen gas while container Y holds pure oxygen gas. If the hydrogen molecules in X

have the same r.m.s. speed as the oxygen molecules in Y, which of the following conclusions may be drawn ?

A. The gas in X has a higher temperature than Y.

B. The gas in X has a higher pressure than Y.

C. The gas in Y has a higher temperature than X.

D. The gas in Y has a higher pressure than X.

E. The gases in X and Y are at the same temperature.

24. (91)

A fixed mass of ideal gas at S.T.P. occupies a volume of 2 m3. The gas is heated and allowed to expand to a final

volume of 4 m3 with its pressure doubled. The root mean square speed of the gas molecules is

A. reduced to one quarter of its original value.

B. halved.

C. unchanged.

D. doubled.

E. increased four times.

25. (91)

Which of the following properties of molecules of an ideal gas is/are the same on the moon as on the earth, if the

temperature and volume of the gas are unchanged ?

(1) The average momentum change when a molecule of the gas rebounds from a wall of the container

(2) The average kinetic energy of a molecule of the gas

(3) The weight of a molecule of the gas


26. (91)

Which of the following statements about an experiment showing the Brownian motion with smoke particles in air

is/are correct?

(1) The motion is caused by collisions between air molecules and smoke particles.

(2) The experiment makes it possible to see the motion of the air molecules.

(3) The motion is irregular because air is a mixture of gases, and the molecules have different masses.


27. (92)

Which of the graphs best represents the distributions of molecular speeds in a gas at 500 K if the dotted curve

represents this distribution for the same gas at 300 K?

A. B. C.

D. E.

28. (92)

Given : Avogadro constant = 6 u 1023 mol-1 Boltzmann constant = 1.38 u 10-23 J K-1

Universal gas constant = 8.31 J mol-1 K-1

If 1 mole of an ideal gas is heated under constant pressure from 20oC to 70oC, the total energy of the gas

molecules is increased by

A. 208 J B. 415 J C. 581 J D. 623 J E. 831 J

MC Question


Container Container

O2

H2

A B

29. (92)

The relative atomic mass of oxygen is 16. What is the ratio of the average speed of oxygen molecules to that of

hydrogen molecules at room temperature?

A. 1/ 16 B. 1/4 C. 1 D. 4 E. 16

30. (93)

Identical containers A and B contain oxygen (O2) and hydrogen (H2) respectively. Both gases are at room

temperature arid atmospheric pressure. Which of the following statements is/are true?

In both containers,

(1) the number of gas molecules is the same;

(2) the r.m.s. speed of gas molecules is the same;

(3) the frequency of collision of gas molecules with the walls of container is the same.


31. (93)

An inexpansible vessel contains air at 50C. What percentage of air remains in the vessel if it is heated to 100C

under constant pressure ?

A. 87% B. 85% C. 73% D. 63% E. 50%

32. (95)

The r.m.s. speed of the molecules of a certain gas X is 341 m s-1 at 298 K. Find the molar mass of the gas X.

(Given : Universal gas constant R = 8.31 J mol-1 K-1 )

A. 5.4 g B. 21.8 g C. 33.8 g D. 42.6 g E. 63.9 g

33. (95)

The pressure of an ideal gas in a container is P. If the number of gas molecules is halved, the volume of the

container is doubled and the temperature is kept constant, the pressure will be

A. P4

1 B. P

2

1 C. P D. 2P E. 4P

34. (97)

Two different ideal gases, A and B, are contained in two identical vessels. If the ratio of their absolute temperature

and the ratio of the root-mean-square speed of the molecules ewe respectively 2 : 1 and 3 : 1, the ratio of their

molecular mass is

A. 2:3 B. 2:9 C. 1:6 D. 9:2 E. 3:2

35. (97)

When a gas is below its critical temperature, which of the following is/are correct ?

(1) Intermolecular forces are significant.

(2) The gas can be liquefied by applying pressure alone.

(3) Collisions between molecules are not perfectly elastic.


36. (98)

The root-mean-square speed of a sample of helium gas molecules, each of mass m, is c. Which of the following

deductions is correct ?

A. The percentage of molecules travelling at speed c is greater than at other speed.

B. Half of the molecules travel at a speed higher than c.

C. All molecules travel randomly with speed c.

D. The average speed of the molecules is c.

E. The average kinetic energy of the molecules is 2

2

1mc .

MC Question


37. (99)

Two metallic containers X and Y of volume V and 4V respectively are connected by a narrow tube as shown.

Initially the tap S is closed and an ideal gas is contained in X at a pressure of 400 kPa while container Y is

evacuated.

The tap S is then opened and when equilibrium is finally reached,

A. the gas pressure in X is 100 kPa.

B. there are still gas molecules moving through the tap S.

C. the product of pressure and volume of the gas in X is equal to that in Y.

D. the density of gas molecules in X is greater than that in Y.

E. the gas molecules in Y on average move faster than those in X.

38. (99)

Which of the following description about ideal gas is/are correct?

(1) An ideal gas obeys Boyle's law only under high temperature and low pressure.

(2) The molecules of an ideal gas have no size.

(3) The internal energy of an ideal gas consists of kinetic energy only.

A. (1) only B. (3) only C. (1) & (2) only D. (2)&(3) only E. (1),(2)&(3)

39. (00)

Which of the following statements concerning a real gas is/are correct ?

(1) Collisions between molecules and the wall of a container are not perfectly elastic.

(2) The volume of the molecules cannot be neglected.

(3) Intermolecular forces cannot be neglected.

A. (1) only B. (2) only C. (3) only D. (1)&(2) only E. (2) & (3) only

40. (01)

Which of the following is NOT a basic assumption of the kinetic theory of an ideal gas?

A. All molecules are in random motion.

B. All molecules move with the same speed at a certain temperature.

C. All molecules are point particles that have no physical size.

D. All collisions are perfectly elastic.

E. All molecules do not exert force on one another except during collisions.

41. (02)

The graph shows the relation between the pressure P and the absolute temperature T of a fixed mass of an ideal

gas, which changes from state A to state B along the path AB. Which of the following statements is/are correct?

(1) The graph shows that P is directly proportional to T.

(2) The volume V of the gas increases.

(3) All the points on straight line AB satisfy the relation T

PV = constant.

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

S

V 4V

X

Y

P

T0

A

B

MC Question


0

p

V1 3 5

5

2

X Y

Z

42. (02)

What is the order of magnitude of the number of molecules in 1 cm3 of air in an atmospheric pressure of 105 Pa

and at room temperature?

(Given: Universal gas constant = 8.31 J K-1 mol-1

Avogadro constant = 6.02 u 1023 mol-1) A. 1025 B. 1019 C. 1016 D. 1013

43. (02)

At 80, the r.m.s. speed of the molecules in a fixed mass of an ideal gas is c. If the temperature is increased to 160, the r.m.s. speed of the gas molecules would become A. 2c. B. 1.4c. C. 1.2c. D. 1.1c.

44. (03)

A fixed mass of an ideal gas undergoes changes from state X to state Z via state Y as shown in the plot of pressure

p against volume V below.

Which graph best shows how the absolute temperature T of the gas varies with its volume V?

A B. C. D.

45. (04)

An ideal gas of volume V and pressure p undergoes a change from state X to state Z via state Y along the path as

shown in the p-V plot.

Which of the following descriptions about the gas at X, Y and Z is correct?

A. The gas is at its coolest at X and is at its hottest at Y.

B. The gas is at its coolest at X and is at its hottest at Z.

C. The gas is at its coolest at Y and is at its hottest at X.

D. The gas has the same degree of hotness at X, Y and Z.

0

T

V1 3 5

X

Y

Z

0

T

V1 3 5

X

Z

0

T

V1 3 5

X

Y

Z

0

T

V1 3 5

X

Z

V

p

0

X

Y

Z

MC Question


46. (04)

In which of the following graphs does the shaded area represent an amount of energy?

(1)

Q = charge on a capacitor

V = p.d. between plates

(2)

e = extension of a wire

F = force causing the extension

(3)

V = volume occupied by a gas

p = pressure exerted by the gas

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

47. (05)

Two vessels contain hydrogen gas and oxygen gas respectively. Both gases are assumed to be ideal and they have

the same pressure and temperature. Which of the following physical quantities must be the same for the two

gases ?

. The volume of the gas B. The mass per unit volume of the gas

C. The r.m.s. speed of the gas molecules

D. The number of gas molecules per unit volume

48. (05)

gas in a vessel of fixed volume leaks gradually. The gas in the vessel changes from state to state along the path shown in the plot of pressure against absolute temperature. What percentage of the original mass of the gas leaks out from the vessel in this process ?

. 10% B. 20% C. 25% D. 50%

49. (06)

The ideal gas equation derived from the kinetic theory can be expressed as p = 2

3

1c

V

Nm.

In this equation, what does the product Nm represent ?

. the total mass of the gas B. the mass of one mole of the gas

C. the number of molecules in unit volume of the gas

D. he number of molecules in one mole of the gas

Answer

1. A 2. E 3. B 4. C 5. B 6. E 7. A 8. D 9. D 10. D

11. B 12. D 13. B 14. E 15. C 16. E 17. B 18. E 19. C 20. D

21. C 22. B 23. C 24. D 25. C 26. A 27. A 28. D 29. B 30. A

31. A 32. E 33. A 34. B 35. C 36. E 37. B 38. D 39. E 40. B

41. D 42. B 43. D 44. C 45. A 46. C 47. D 48. C 49. A

0

V

Q 0

F

e 0

p

1/V

0 T 2T

p

1.5 p

Pressure

X

Y

Absolute Temperature

Out of Syllabus

MC Question


MC Question

Chapter 2 Kinematics (MC)2P1

1. (80)

The displacement y of a point P on a plucked string varies with time t as shown in the graph above. Which of the

following correctly shows the variation of the velocity v of the point P with time?

A. B. C. D. E.

2. (82)

Two bodies X and Y are moving with constant velocities in the directions indicated by the arrows. At time t = 0,

they are at the positions shown. At time t.= 2 s, the magnitude of the velocity of Y relative to X is

A. 4 m s-1 B. 5 m s-1 C. 6 m s-1 D. 8 m s-1 E..10 m s-1

3. (83)

A ball bounces up and down from the floor. Which of the following graphs shows the variation of the velocity v

with time t?

A. B. C. D. E.

4. (83)

A man is walking due east at 1.00 m s-1 on the deck of a ship steaming north at 1.73 m s-1. In what direction will

the man be walking relative to the surface of the earth ?

A. N 30o E B. N 60o E C. NE D. N26.9o E E. N40.9o E

5. (83)

The velocity v of a particle varies with time t as shown. Which of the following graphs best represents the

variation of the displacement s of the particle with time t ?

A. B. C. D. E.

y

t

v

t

v

t

v

t

v

t

v

t

v

t

v

t

v

t

v

t

v

t

3 m s-1

4 m s-1

6m

X Y

0

v

t

v

t0

v

t

0

v

t0

s

t0

s

t0

s

t0

s

t0

0

v

t

0

v

t

s

t0

Out of Syllabus

Out of syllabus

MC Question


6. (86) (88)

A football player is running at a velocity of 3 m s-1 due north. After a violent collision with another player, he is

moving at a velocity of 4 m s-1 due east. Which of the following arrows best represents the direction of his change

of velocity?

A. B. C. D. E.

7. (88)

A boy wished to swim across a river with parallel banks as shown in the diagram below. Assuming the water is

flowing at 0.5 m s-1, and the swimming speed of the boy is 1 m s-1, along which direction should the boy swim if

he wishes (1) to reach the opposite bank in the shortest time; and (2) to take the shortest route to the opposite

bank?

(l) shortest time (2) shortest route

A. X Y

B. X Z

C. Y X

D. Y Z

E. Z Y

8. (89)

A ball bounces up and down on the ground in the vertical direction. Which of the following graphs best describes

the variation of its acceleration a with time t ?

A. B. C.

D. E.

9. (89)

Two ships X and Y travel with equal speeds. X moves due North and Y moves due East. Which of the following

best gives the direction of the velocity of X relative to Y?

A. B. C. D. E.

10. (90)

When a man is running due north, he feels that the wind is blowing towards him from the east. What is the actual

direction of the wind ?

A. from the east B. from north-east C. from south-east

D. from south-west E. from north-west

water

current Z Y X

a

t0

a

t

0

a

t

0

a

t

0

a

t

0

out of syllabus

Out of syllabus

MC Question


11. (98)

The velocities of the longitudinal and transverse waves produced by an earthquake are 5.0 km s-1 and 9.0 km s-1

respectively. A seismograph records the arrival of the transverse waves 64 s before that of the longitudinal waves.

How far away was the earthquake ?

A. 256 km B. 320 km C. 576 km D. 659 km E. 720 km

12. (01)

An object accelerates uniformly along a straight line from X to Z. It passes X and Z with speeds u and v

respectively. What is its speed when it passes Y, which is the mid-point of XZ?

A. 2

22vu

B. uv

C. vu

uv

2

D. 2

vu

E. It cannot be found as the distance between X and Z is not known.

13. (02)

Two small identical objects P and Q are released from rest from the top of a building 80 m above the ground. Q is

released 1 s after P. Neglecting air resistance, what is the maximum vertical separation between P and Q in the

air?

A. 5 m

B. 10 m

C. 35 m

D. 45 m

Answer

1.B 2.B 3.B 4.A 5.B 6.A 7.D 8.C 9.C 10.C 11.E 12.A 13.C

X Y Z

MC Question

Chapter 4,5 Newtonian Mechanics (MC)4P1

1. (80)

A body is subjected to an applied driving force F and a constant resistive force. Which of the graphs below

represents the variation of the acceleration a of the body with the applied driving force F ?

A. B. C. D. E.

2. (82)

A solid of mass m starts from rest and travels for a given time under the action of a given force. The speed which

it acquires is proportional to

A. m B. m

1 C. m D.

m

1 E. m2

3. (82)

A builder using a pulley system to lift a bucket of cement of weight 150 N exerts a steady force F and pulls 30 m

of rope through the system in order to raise the bucket 10 m. The friction in the system is small but NOT

negligible. The value of the force F is most probably

A. less than 50 N.

B. exactly equal to 50 N.

C. between 50 N and 150 N.

D. between 150 N and 450 N.

E. more than 450 N.

4. (83)

A spaceship burns fuel and moves with constant acceleration in a straight line. Which of the graphs below best

represents the variation of its momentum p with time t?

A. B. C. D. E.

5. (83)

A ball bounces up and down from the floor. Which of the following graphs shows the variation of the velocity v

with time t?

A. B. C. D. E.

6. (84)

A horizontal force P is applied to a wooden block at lest on a rough horizontal table. P is increased uniformly

from zero. Which of the following graphs best describes the variation of the friction F acting on the block with

P ?

A. B. C. D. E.

a

F

0

a

F

0

a

F

0

a

F

0

0

p

t0

p

t

0

v

t

v

t0

v

t

0

P

0

F

P

0

F

P

0

F

P0

F

P0

F

P

a

F

0

0

p

t0

p

t

0

p

t

0

v

t

0

v

t

Out of syllabus

Out of syllabus

MC Question


7. (85)

A lift of mass M carries a man of mass m. When the lift is being hauled upward by a rope, the lift rises with an

acceleration a. The reaction between the man and the floor of the lift is

A. mg B. m(g - a) C. m (g + a) D. m(g + a) - Ma E. m(g + a) + Ma

8. (85)

Two bodies P and Q are connected by a light string A. The weights of P and Q

are 4 N and 10 N respectively. P is connected to the roof by another light string

B. If string B is cut and the bodies are allowed to fall, the net force acting on P

during free fall is

A. 0 N. B. 4 N C. 6 N D. 10 N E. 14 N

9. (86)

A small block M of mass 1 kg is transported across a small hill along the road ABC by an applied force F which is

always parallel to the road. The speed of M is kept constant throughout the journey and the kinetic friction

between the block and the road is 2.60 N. The total work done by F in transporting M from A to C is

A. Zero. B. 104 J. C. 152 J. D. 200 J. E. 304 J.

10. (86)

An object of mass 3 kg is placed on a smooth plane inclined at 30o to the

horizontal. It is connected by a light string passing over a frictionless pulley to

another object, of mass 2 kg, as shown below. When the system is released the

tension in the string will be

A. 18 N. B. 20 N. C. 24 N. D. 25 N. E. 30 N.

11. (87)

An object of mass 3 kg is tied to another object of mass 2 kg with a string passing

over a fixed smooth pulley. The weight of the pulley is negligible. When the

objects move under the action of gravity, the vertical upward force acting on the

axle of the pulley is

A. zero. B. 10 N. C. 24 N. D. 48 N. E. 50 N.

12. (87)

Steel ball bearings, each of mass m, are fired at the rate of n ball bearings per second towards a fixed vertical steel

block with a horizontal speed v. They rebound from the block with the same speed. The average force exerted on

the block is

A. zero. B. m n v. C. 2 m n v. D. m g n v. E. 2 m g n v.

13. (88)

A smooth block of mass 2 kg slides down a wedge. The wedge, of mass 10 kg, is placed on a horizontal table, and

its inclined plane makes an angle of 30o with the horizontal. If the wedge remains stationary all the time, the

normal reaction of the table acting on the wedge is

A. 15 N. B. 85 N. C. 100 N. D. 115 N. E. 120 N.

B

P

A

Q

A

B

C

M

10m

30o 30o

2 kg

3 kg

30o

3 kg 2 kg

axle

MC Question


14. (88)

A force F is applied to an initially stationary particle from time t = 0. F varies sinusoidally with time t as shown in

the following graph:

Which of the following graphs best represents the variation of the subsequent velocity v of the particle with t ?

A. B. C. D. E.

15. (89)

Two objects of weights 2 N and 3 N are suspended from a fixed point by two

identical light springs A and B as shown in the diagram. The force constants of

the springs are both 1 N cm-1. What are the extensions of springs A and B ?

Extension of spring A Extension of spring B

A. 5 cm 3 cm

B. 5 cm 2 cm

C. 3 cm 2 cm

D. 3 cm 5 cm

E. 2 cm 3 cm

16. (89)

In the figure above, X and Y are blocks of mass 1 kg and 2 kg respectively. S is a spring balance of negligible

mass and P is a smooth pulley fixed at the top of two smooth inclined planes. What is the reading of S when X is

held stationary ?

A. 5 N B. 10 N C. 15 N D. 20 N E. 30 N

17. (89)

A man weighs an object with a spring balance in a lift. Before the lift moves the scale reads 50 N. The lift goes

down and then stops. The reading on the scale is

A. 50 N throughout the journey.

B. more than 50 N when the lift starts, and remains steady until it comes to rest.

C. less than 50 N when the lift starts, and remains steady until it comes to rest.

D. more than 50 N as the lift starts, and less than 50 N as it comes to rest.

E. less than 50 N as the lift starts, and more than 50 N as it comes to rest.

18. (91)

An object of mass m slides with constant acceleration a down a plane making an angle T with the horizontal. The frictional force acting on the object is

A. mg ma B. mg ma sinT C. Mg sinT ma D. (mg ma) sin T E. (mg + ma) sinT

F

t

0

v

t

0

v

t

0

v

t

v

t

0

2 N

spring A

3 N

spring B

X

30o 30o

P

Y

S

v

t

0

Out of syllabus

Out of syllabus

MC Question


19. (92)

A man in a lift measures his weight with a compression balance and discovers that his weight is reduced by 10%.

The lift is probably

(1) moving upwards and accelerating at g/10.

(2) moving upwards and decelerating at g/10.

(3) moving downwards and accelerating at g/l0.

(4) moving downwards and decelerating at g/10.

(5) moving downwards with uniform velocity.

A. (l) & (3) only B. (1) & (4) only C. (2) & (3) only D. (2) & (4) only E. (5) only

20. (92)

Three blocks A, B and C of masses m, 2m and 2m respectively are placed on a smooth horizontal ground as shown

in the figure above. A constant horizontal force is applied to block A so that the three blocks move with the same

acceleration towards the right. What is the resultant force acting on block B ?

A. F/5 B. F/3 C. 2F/5 D. 3F/5 E. F

21. (92)

A simple pendulum is swinging in a vertical plane. When it is at the position shown, which of the following

diagrams best represents the forces acting on the bob? Neglect air friction.

A. B. C. D. E.

22. (93)

The resultant of two forces F1 and F2 acting at a point has a minimum value of 1 N and a maximum value of 7 N.

When the two forces act at right angles to each other, the magnitude of their resultant is

A. 3 N B. 5 N C. 6 N D. 50 N E. 8 N

23. (93)

A box moves at a uniform velocity of 2 m s-1 on a frictionless horizontal surface. Sand falls into the box with

negligible speed at a rate of 90 kg per minute. What horizontal force is required to keep the box moving uniformly

at 2m s-1 ?

A. 0 N B. 3 N C. 6 N D. 90 N E. 180 N

B CA

F

F2

F1

MC Question


24. (94)

A man of weight W stands on a compression balance placed inside a lift. The velocity-time graph of the lift is

shown below. (The upward direction is taken to be positive.)

Which of the following graphs best shows the variation of the reading on the balance, R, with time, t ?

A. B. C. D. E.

25. (94)

The above figure shows a propeller-motor system connected by a light, rigid rod to a fixed point P on the ceiling.

The system remains stationary when the motor is on. Which of the following diagrams correctly represents the

forces acting on the propeller-motor system ?

A. B. C. D. E.

26. (94)

When an object falls freely, its total energy

A. increases during the fall.

B. decreases during the fall.

C. remains constant during the fall.

D. is zero at the beginning of the fall.

E. is at a maximum at the end of the fall.

27. (95)

When given a slight push, a toy car moves freely with constant velocity down a plane inclined at 20o to the

horizontal. If the mass of the car is 0.5 kg, find the force parallel to the inclined plane for pulling the car up the

plane with constant velocity.

A. 1.7 N B. 3.4 N C. 4.7 N D. 6.7 N E. 9.4 N

28. (95)

Two small spheres A and B of masses 1 kg and 2 kg respectively are released from

rest at heights 4h and h above the ground as shown. Which of the following

statements is/are correct ? (Assume air resistance is negligible.)

(1) The acceleration of sphere A doubles that of sphere B.

(2) The time taken for sphere A to reach the ground is double that of

sphere B.

(3) The kinetic energy of sphere A when reaching the ground is double

that of sphere B.


velocity

time0 t1 t2

R

t

0 t1 t2

W

R

t

0 t1 t2

W

R

t

0 t1 t2

W

R

t

0 t1 t2

W

R

t

0 t1 t2

W

P

motor

propeller

rod

4h

h

A

B

MC Question


29. (96)

The figure shows two blocks A and B, each of mass m, connected by two

light springs to a fixed support. Each spring has a force constant k. What is

the total extension of the system when it is at static equilibrium ?

A. mg/(2k) B. mg/k C. 3mg/(2k)

D. 2mg/k E. 3mg/k

30. (96)

Which of the following pairs of quantities of a moving object must be in the same direction?

(1) acceleration and change in momentum

(2) displacement and velocity

(3) velocity and acceleration

A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only E. (1),(2) & (3)

31. (97)

Two wooden blocks A and B are connected by a string which passes over a smooth, fixed pulley as shown. The

maximum friction between any two surfaces is 2 N. If a horizontal force F is applied to block B, find its minimum

value for moving B.

A. 2 N B. 4 N C. 6 N D. 8 N E. 10 N

32. (98)

Two identical light springs are connected with two masses of 1.0 kg and 0.5 kg as

shown. Which of the following statements is/are correct ?

(1) The tension in the upper spring is double that in the lower spring.

(2) The force acting on the ceiling by the whole system is 15 N.

(3) The tension in the upper spring will remain unchanged if the two masses

are exchanged in position.

A. (1) only B. (3) only C. (1) & (2) only

D. (2) & (3) only E. (1), (2) & (3)

33. (98)

Two blocks A and B of mass ratio 1:2 are placed on a horizontal frictionless surface as shown above P and Q are

horizontal forces acting on A and B respectively (with P > Q ) so that the blocks move to the right with constant

acceleration. Find the force acting on B by A.

A. 3

QP B.

3

QP C.

3

)(2 QP D.

3

2 QP E.

3

2QP

34. (98)

The initial momentum of an object is 2 N s in the direction S 45oE and its final momentum is 1 N s due east. If

this change takes place in 0.5 s, the average force acting on the object during the change is

A. 1 N due north

B. 1 N due south

C. 0.5 N due north

D. 2 N due south

E. 2 N due north

A

B

B

AF

1.0 kg

0.5 kg

A BP Q

45o

initial

momentum

final

momentum North

Out of syllabus

MC Question


35. (98)

The graph shows the time variation of the net force, F, acting on an object of mass 1 kg. The object is initially at

rest and its subsequent motion is along a straight line. Which of the following statements is/are correct ?

(1) The object is accelerating in the first 5 seconds.

(2) The maximum speed of the object is less than 10 m s-1.

(3) The final speed of the object is zero.

A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only E. (1), (2) & (3 )

36. (99)

A block of mass 5 kg is placed on the inclined surface of the wedge shown above. All contact surfaces are

assumed to be smooth. What is the magnitude of the horizontal force F exerted on the wedge so that it remains

stationary while the block is sliding down the inclined surface with acceleration ?

A. 0 N B. 18 N C. 24 N D. 30 N E. 32 N

37. (99)

Two objects A and B of equal mass m are connected by two identical light springs and are placed on a horizontal

smooth surface. A horizontal force F is applied to B so that the system is in equilibrium. If the applied force F is

suddenly removed, what are the magnitudes of the acceleration of each object at the instant when force F is

removed ?

Acceleration of A Acceleration of B

A. zero m

F

B. zero zero

C. m

F

2

m

F

D. m

F zero

E. m

F

m

F

38. (99)

The above graph shows the variation of kinetic energy E with the square of velocity v of a moving mass m. What

is the momentum of the mass when it is moving at a speed of 2 m s-1?

A. 1 N s B. 2 N s C. 4 N s D. 8 N s E. 16 N s

F/N

t/s0

4

5

horizontal

surface

F

40 cm

30

cm

A B

F

E / J

v2 / m2 s-2

0

1

1

Out of syllabus

MC Question


39. (00)

Two books A and B are placed on a horizontal table surface as shown. A horizontal force F is applied to A but the

system remains stationary. Which of the following statements is/are correct ?

(1) The frictional force acting on B by the table surface is greater than F

(2) The frictional force acting on A by B is towards the left.

(3) The system would remain stationary if F is applied to B instead.

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)

40. (00)

A student holds one end of a string to which a block of mass 8 kg is tied at the other end. He raises the block with

an acceleration by pulling the string in an upward direction. If the maximum tension that the string can withstand

is 120 N, find the maximum acceleration of the block before the string breaks.

A. 5.0 m s-2

B. 7.5 m s-2

C. 10.0 m s-2

D. 12.5 m s-2

E. 15.0 m s-2

41. (00)

A trolley of mass 0.5 kg moves with a certain acceleration down a runway which is inclined to the horizontal at

15o. If the angle of inclination is increased to 20o the acceleration of the trolley would be doubled. Find the

average frictional force, assuming the same in both cases, acting on the trolley.

A. 0.72 N B. 0.80 N C. 0.88 N D. 0.96 N E. 1.04 N

42. (00)

Two objects A and B of masses m and 2m respectively are initially at rest on a smooth, horizontal surface. If each

of them is acted upon by the same force for the same period of time, the ratio of the gain in kinetic energy of A to

that of B is

A. 2:1 B. 1:2 C. 1:1 D. 1:4 E. 4:1

43. (00)

A light spring is fixed to the bottom of a vertical tube. A ball is released from rest at a

height h above the upper end of the spring as shown. After rebounding several times

the ball eventually comes to rest and stays on top of the spring. Assume all contact

surfaces are smooth and the spring obeys Hooke's law throughout. Which of the

following statements is/are correct ?

(1) The compression of the spring is proportional to the mass of the ball.

(2) The compression of the spring is independent of the height h.

(3) The gravitational potential energy lost by the ball is equal to the strain energy

stored in the spring.

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)

1.A 2.B 3.C 4.D 5.B 6.D 7.C 8.B 9.B 10.A 11.D 12.C 13.D 14.D 15.A

16.B 17.E 18.C 19.C 20.C 21.A 22.B 23.B 24.D 25.D 26.C 27.B 28.D 29.E 30.A

31.C 32.D 33.D 34.E 35.C 36.C 37.A 38.C 39.D 40.A 41.C 42.A 43.C

B

AF

h

Out of syllabus

MC Question

Chapter 6 Linear Momentum (MC)6P1

1. (80)

A particle of mass m strikes a barrier with speed v and rebounds with the same speed v. Which of the following

statements is/are correct ?

(1) The angle I must be equal to the angle T. (2) The change in the component of momentum pcrpendicular to the barrier is 2 m v sin T. (3) The change in the component of momentum parallel to the barrier is zero.

A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only E. .(1), (2) & (3)

2. (81)

Before the start of a race, the momentum of each competitor is less than his momentum during the race. Which of

the following statements is/are correct ?

(1) This situation violates Newton's law of conservation of momentum.

(2) The law of conservation of momentum applies only to collisions between two objects.

(3) A force acts on each competitor to increase his momentum as he starts to race.


3. (82)

Two objects of masses m and 4m move towards each other along a straight line with kinetic energies E and 4E

respectively. The total linear momentum of both masses taken together is

A. 3 mE2 B. 4 mE2 C. 5 mE2 D. 15 mE2 E.17 mE2

4. (83)

A sphere X of mass m, travelling with speed u, makes a head-on collision with a similar sphere Y which is at rest.

After the collision the velocities of X and Y are v1 and v2 respectively. Which one of the following is a possible

pair of values for v1 and v2 ?

v1 v2

A. - u 2 u

B. u / 4 3 u /4

C. 3 u / 4 u / 4

D. 2/u 2/u

E. u / 2 2/3u

5. (84)

In an inelastic collision between two bodies, and in the absence of external forces,

A. kinetic energy and momentum are both conserved.

B. kinetic energy is not conserved but momentum is conserved.

C. kinetic energy is conserved but momentum is not conserved.

D. neither kinetic energy nor momentum is conserved.

E. kinetic energy is not conserved and the momentum changes direction.

6. (84)

An alpha particle collides with a stationary helium nucleus ( He42 ) in a cloud chamber. Which of the following

diagram represents the most probable set of tracks ?

A. B. C. D. E.

vv

T I

D

D

He42 D

D

He42D D

He42

DD

He42 D

D

He42

MC Question


7. (86)

A sphere X moving with velocity a on a smooth horizontal plane makes a head-on collision with another sphere Y

of the same mass which is initially at rest. If the collision is perfectly elastic, which of the following statements

is/are correct ?

(1) Kinetic energy is conserved in this collision.

(2) Linear momentum is conserved in this collision.

(3) X and Y stick together and move off with the same velocity after the collision.


8. (91)

A gas atom of mass m moving with a uniform speed v makes an elastic collision with the wall of the container as

shown in the diagram. What is the magnitude of the change in the momentum of the gas atom ?

A. 2 m v B. m v sin T C. m v cosT D. 2 m v sinT E. 2 m v cosT

9. (94)

A softball of mass 0.5 kg flies horizontally with a speed of 20 m s-1 towards a player. After being hit by the bat, it

flies away at 30 m s-1 perpendicular to its original direction. Find the magnitude of the impulse acting on the

softball.

A. 5 kg m s-1 B. 18 kg m s-1 C. 20 kg m s-1 D. 25 kg m s-1 E. 36 kg m s-1

10. (95)

A trolley travels with constant velocity to the right on horizontal ground and collides with a light helical spring

attached to a wall fixed to the ground (earth) as shown. At the instant that the trolley comes momentarily to rest

during collision, what has happened to the initial momentum of the trolley ?

A. It has been transferred to the earth.

B. It has been stored in the spring.

C. It has been dissipated as sound and heat.

D. It has been destroyed by the friction due to the ground.

E. It has been lost because the collision was not perfectly elastic.

11. (96)

X, Y and Z are three spheres of the same size but with masses m, m and 2m respectively, lying on a smooth

horizontal track with Y and Z in contact as shown. X is moving to the right with velocity u and makes a head-on

collision with Y. If all collisions are perfectly elastic, which of the following gives the possible velocities of the

three spheres after all collisions ? (Take to the right as positive.)

X Y Z

A. 0 0 u/2

B. 0 u/3 u/3

C. -u/3 0 2u/3

D. 0 -u/3 2u/3

E. u/4 u/4 u/4

m m 2m

u

X Y Z

MC Question


12. (97)

A ball of mass m is projected vertically downwards with speed v from a certain height and rebounds from the

ground back to the same height. Which of the following statements is/are correct ? (Neglect air resistance.)

(1) The collision between the ball and the ground is not perfectly elastic.

(2) The loss in energy of the ball in the collision is 2

2

1mv .

(3) If the ball is projected vertically upwards from the same height with the same speed, it would rebound

to a greater height.


13. (97)

A nucleus originally at rest splits into two fragments of unequal mass. The fragment with smaller mass has a

larger

(1) momentum.

(2) speed.

(3) kinetic energy.


14. (99)

The above figure shows an open wagon moving with negligible resistance in vertically falling rain. An

appreciable amount of rain falls into the wagon and accumulates there. What are the effects of the accumulating

rain on the speed, momentum and kinetic energy of the wagon? (Ignore the effects of the rain drops hitting the

front of the wagon.)

speed momentum kinetic energy

A. decreased unchanged decreased

B. decreased unchanged unchanged

C. decreased decreased decreased

D. unchanged unchanged unchanged

E. unchanged increased increased

15. (02)

P, Q and R are three identical spheres moving with the same speed along a smooth horizontal track. They undergo

head-on elastic collisions with spheres X, Y and Z respectively which are initially at rest. After collision, P

continues to move in its original direction, Q becomes stationary while R reverses its motion. After collision,

which sphere (X, Y or Z) has the greatest magnitude of

(1) momentum

(2) kinetic energy?

(1) (2)

A. Y Z

B. Y Y

C. Z X

D. Z Y

MC Question


16. (02)

The impulse experienced by an object is equal to its change in

A. momentum. B. kinetic energy. C. velocity. D. acceleration.

17. (04)

Two spheres A and B of the same size, which have masses m and M respectively. A moves horizontally with a

speed u and makes a head-on elastic collision with B, which rests on a smooth horizontal surface as shown. Referring

to each of the following descriptions about B, how is m compared with M?

(1) B attains the greatest kinetic energy after collision

(2) B attains the greatest magnitude of momentum after collision

(3) B attains the greatest speed after collision

(1) (2) (3)

A. M = m M = m M m

C. M = m M >> m M m M

MC Question

Chapter 3 Projectile motion (MC)3P1

1. (80)

A metal sphere is released from rest and allowed to fall vertically under gravity through oil. Which of the

following statements is/are correct?

(1) The acceleration decreases as the speed increases.

(2) At the terminal speed, the upward forces on the sphere have their maximum values.

(3) If the sphere were dropped in air instead of in oil, there would be no terminal speed.


2. (81)

Projectiles X and Y are launched simultaneously from the top of a cliff. Suppose X is launched horizontally with

speed 20 m s-1, and Y is launched at an angle of 60o above the horizontal with speed 40 m s-1. (The motion of both

X and Y is in the same plane.) Which of the following statements is/are correct ?

(1) X and Y travel equal vertical distances in equal times.

(2) X and Y travel equal horizontal distances in equal times.

(3) X and Y never meet.


3. (83)

A particle is released from X and slips down a smooth curve to Y, at the edge of a table 2 m high, where it travels

horizontally. It then leaves the table and travels freely under gravity, until it hits the ground at Z, at a horizontal

distance of 3 m from Y. The vertical distance, h, of X above Y is

A. 9/8 m B. 4/3 m C. 2 m D. 3 m E. 4 m

4. (84)

An object is thrown horizontally from the top of a cliff at a speed of 20 m s-1. What will be the speed of the object

after 3 s ?

A. 20m s-1 B. 25m s-1 C. 30m s-1 D. 36m s-1 E. 50m s-1

5. (84)

The velocity v of a small steel ball falling in a viscous liquid inside a long vertical tube varies with time t, as

follows:

Which of the following graphs best represents the variation of the viscous force F acting on the body?

A. B. C. D. E.

6. (87)

A sphere is projected downwards from A with a speed of 10 m s-1 at

an angle of 30o to the horizontal. The sphere rebounds from the

ground, first at B and then at C. If the collisions are perfectly elastic,

the horizontal distances BC is equal to

A. 8.7 m. B. 10.0 m. C. 26.0 m. D. 43.5 m. E.100.0 m.

2 m

h

X

Y

Z

3 m

0

v

t

0

F

t0

t

F

0

t

F

0

t

F

0

t

F

A

B10 mC

MC Question


P

Q

7. (87)

A parachutist of mass m falls in air under the influence of gravity. The air resistance is equal to bv, where v is his

speed and b is a constant. After falling a height s from rest, he reaches a terminal speed u. His kinetic energy at

that instant is

A. mgs. B. mgs bus. C. mgs (m3 g2)/(2b2) D. mgs + (m3 g2)/(2b2) E. m3 g2 / (2b2)

8. (90)

A hunter aims his gun at a target which is at rest at point M, and his gun

makes an angle T with the horizontal. Exactly as the gun is fired the target drops from M with zero initial velocity. If t he bullet is to strike the

target, the angle T depends on (1) u, the initial speed of the bullet.

(2) h, the vertical height of the target above the level of the gun.

(3) d, the horizontal distance of the gun from the target.

A. (1) only B. (3) only C. (1) & (2) only

D. (2) & (3) only E. (1), (2) & (3)

9. (91)

A spacecraft of mass 4.0 u 104 kg was travelling on its way to the moon with the rocket motors shut down. At the instant when it was travelling at 1500 m s-1, the rocket motors were turned on for 5 seconds to make a course

correction. If the rocket gave a thrust of 1.0 u 105 N at right angles to the direction of travel, throughout what angle would the flight path of the spacecraft be turned ?

A. 1.6 u 10-3 rad B. 5.7 u 10-3 rad C. 8.3 u 10-3 rad D. 1.6 u 10-2 rad E. 8.3 u 10-2 rad

10. (92)

A ball-bearing is dropped into viscous oil. Which of the following correctly describes its motion before the

terminal speed is reached ?

Velocity Acceleration

A. decreases decreases

B. decreases increases

C. increases constant

D. increases decreases

E. increases increases

11. (93)

Two identical coins P and Q are placed at the edge of a table. At the same

instant, P is pushed slightly and falls vertically to the ground while Q is

projected horizontally and reaches the ground through a parabolic path (as

shown). Which of the following statements is/are correct? (Neglect air

resistance)

(1) P and Q reach the ground at the same time.

(2) P and Q have the same acceleration.

(3) P and Q have the same vertical speed on reaching the ground.


12. (94)

Three bombs are released from a bomber flying horizontally with constant velocity to the right. They are released

from rest (relative to the bomber) one by one at one-second intervals. Neglecting air resistance, which of the

following diagrams correctly shows the positions of the bomber and the three bombs at a certain instant?

A. B. C. D. E.

gun

d

u T

h

M

MC Question


13. (96)

An object is thrown vertically upward and experiences an air resistance opposing its motion with magnitude

proportional to its speed. Which of the following graphs best represents the variation of the acceleration, a, of the

object with time, t, starting from the moment when the object leaves one's hand up to the time when it returns the

ground ? (Take downward as positive.)

A. B. C. D. E.

14. (96)

A particle is projected horizontally from a table with an initial speed u and attains a speed v Just before hitting the

ground. What is the time of flight of the particle? (Neglect air resistance.)

A. g

v B.

g

uv C.

g

uv

2

22

D. g

uv 22 E. It cannot be found as the vertical distance fallen is not known.

15. (98)

A small object is thrown horizontally towards a vertical wall 1.2 m away. It hits the wall 0.8 m below its initial

horizontal level. At what speed does the object hit the wall ? (Neglect air resistance.)

A.2 m s-1 B. 3 m s-1 C. 4 m s-1 D. 5 m s-1 E. 7 m s-1

16. (01)

A stone is projected at an angle of 45q to the horizontal with an initial kinetic energy E. Neglecting air resistance, when the stones is halfway up, its kinetic energy is

A. 4

E.

B. 2

E.

C. 4

3E.

D. 2

E.

E. E .

0t

a

g

-g

0t

a

g

-g

0t

a

g

-g

0t

a

g

-g

0t

a

g

-g

1.2 m

wall

0.8 m

MC Question


17. (03)

The figure shows part of the stroboscopic picture of a particle initially projected horizontally into the air. The side

of each square of the grid is 5 cm long. Estimate the frequency of the strobe lamp used.

(Neglect air resistance.)

A. 5.8 Hz

B. 7.1 Hz

C. 10.0 Hz

D. 12.5 Hz

18. (04)

The figure shows the barrel of a gun that aims directly at a point P 40 m from the muzzle of the gun. The barrel

makes an angle T with the vertical.

If the speed of the bullet is 50 ms-1 when it leaves the gun, calculate the separation between the bullet and point P

when the bullet is vertically below P. (Neglect air resistance.)

A. 3.2 m

B. 4.8 m

C. 7.8 m

D. It cannot be found as the value of T is not known.

Answer 1.C 2.D 3.A 4.D 5.A 6.C 7.E 8.D 9.C 10.D

11.E 12.D 13.C 14.D 15.D 16.C 17.C 18.A

5 cm

5 cm

MC Question

Chapter 7 Circular motion (MC)7P1

1. (80)

Racing tracks for cars are banked on the corners at an angle to the horizontal. Which of the following is a possible

reason for this design feature ?

(1) To reduce the frictional force between the car and the track necessary to prevent skidding.

(2) To reduce the radius of curvature of the path which a car travelling at a given speed can safely follow.

(3) To increase the component of the weight of the car towards the centre of its path.


2. (82)

A stone of weight W tied to a piece of string is swung in a vertical circle. At the topmost point of is path, the

tension in the string is T and the centripetal force is F. Which of the following statements is true?

A. F = W + T.

B. F = W T.

C. The net force acting downwards on the stone is F+ T+ W.

D. The net force acting downwards on the stone is F T + W.

E. The net force acting downwards on the stone is F T W.

3. (83)

A boy is whirling a stone, tied to a piece of string, in a vertical circle as shown above. The string suddenly breaks

at P. Which of the paths (I - V) represents a possible path for the stone from just before the string breaks until the

stone hits the ground ?

A. I B. II C. III D. IV E. V

4. (84)

The diagrams represents the rear view of a motorcar moving, away from an observer, on a level road at a constant

speed around a bend of which the centre of curvature is at P. Which of the arrows best represents the direction of

the resultant of the forces exerted by the road on the car ?

A. B. C. D. E.

5. (86)

A particle is placed at a height h on a smooth loop-the-loop track, as shown. The radius of the loop is r. P is now

released from rest. If P is to complete the loop, the minimum value of h should be

A. 2r. B. 2.5r. C. 3r. D. 4r. E. 5r.

V

I II

III IV

P

P

h

MC Question


6. (88)

A car of mass m travels into a region where the track is an arc of a vertical circle of radius r. At the bottom of this

arc, the car travels at speed v. At this position the vertical force exerted upwards by the track on the car is

A. mv2/r. B. mg. C. mv2/r mg. D. mg mv2/r E. mg + mv2/r

7. (89)

A smooth conical container rotates about the axis AB as shown. A marble remains at rest relative to the container

at a radial distance r from the axis. If the velocity of the marble is v, then v2 is equal to

A. g r sin 30o B. g r tan 30o C. g r /tan 30o D. g r cos 30o E. g r / cos 30o

8. (90)

A spring of unstretched length 10.0 cm, has one end fixed to the ceiling. A mass is suspended at the other end, and

the extension so produced is 3.0 cm. When the mass is set to rotate in a horizontal circular path the length of the

spring is 16.0 cm. The angle between the spring and the vertical is

A. 15o B. 30o C. 45o D. 60o E. 75o

9. (91)

The diagram shows part of the route of a roller-coaster in an amusement park. The cart descends from H,

completes a circular loop A and moves to B. If the cart of passengers is to complete the central circular track

safely, what is the minimum velocity of the cart at the bottom of the circular track A? (Assume that there is no

friction between the cart and the track.)

A. 10 m s-1 B. 20 m s-1 C. 22.4 m s-1 D. 24.5 m s-1 E. 30 m s-1

10. (93)

The figure shows a small heavy bob P attached to a fixed point A on the ceiling by a light inextensible string. The

bob is pulled aside with the string taut and then released from rest. Which of the following descriptions is/are

true?

(1) When moving towards the lowest point of its path, the angular speed of the bob is increasing.

(2) The centripetal acceleration of the bob is constant.

(3) When the bob is at the lowest point, the tension in the string equals the centripetal force.


A

P

Out of syllabus

Out of syllabus

MC Question


11. (94)

A student whirls a small bucket of water in a vertical circle of radius 0.6 m. For no spilling, what is the minimum

speed of the bucket at the highest point of its path ?

A. 2.45 m s-1 B. 3.46 m s-1 C. 4.08 m s-1 D. 4.90 m s-1 E. 5.77 m s-1

12. (95)

A small object with a mass of 0.05 kg is released from rest at the rim of a heavy, smooth semi-spherical bowl of

radius 10 cm. Find the force acting on the object by the bowl when it passes the bottom of the bowl.

A. 0.5 N B. 1.0 N C. 1.5 N D. 2.0 N E. 2.5 N

13. (95)

An aircraft flies along a horizontal circle of radius 10 km with a constant speed of 155 m s-1. Calculate the angle

between its wings and the horizontal.

A. 11.5o B. 12.0o C. 12.5o D. 13.0o E. 13.5o

14. (96)

A small object P of mass 0.3 kg is attached to one end of a light, rigid rod of length 0.5 m, which is free to rotate

about the other end O as shown, in the above figure. The object is swung to rotate in a vertical circle so that it

attains a speed of 2 m s-1 at its topmost position. What is the force exerted on one end of the rod at this instant?

A. a compressive force of 0.6 N

B. a tensional force of 0.6 N

C. a tensional force of 2.4 N

D. a tensional force of 5.4 N

E. a compressive force of 5.4 N

15. (97)

The figure shows a car moving round a comer with a radius of 8 m on a banked road of inclination 20o At what

speed would there be no friction acting on the car along OA ?

A. 5.0 m s-1 B. 5.2 m s-1 C. 5.4 m s-1 D. 5.6 m s-1 E. 5.8 m s-1

16. (97)

A ball bearing is released from rest at a height h on a smooth track and completes the circular loop of the track. If

R is the reaction acting on the ball bearing at the highest point A of the loop, which of the following graphs

correctly shows the variation of R with h ?

A. B. C. D. E.

20o

O

A8 m

centre of mass

hA

0

R

h0

R

h

0

R

h

0

R

h

0

R

h

P

O

0.5m

Out of syllabus

Out of syllabus

Out of syllabus

MC Question


17. (99)

A small ball-bearing is projected with velocity v from the lowest position P of a vertical circular track which is

not smooth. The ball-bearing starts to leave the track at Q. Which of the following diagrams best represents all the

forces acting on the ball-bearing at Q?

A. B. C. D. E.

18. (00)

A car of mass m is moving with speed v on a banked road along a circular path of horizontal radius r. The angle of

inclination of the road is T. If the centripetal force arises entirely from a component of the normal reaction N from the road, which of the following relations is correct ?

A. N cosT = mg B. N = mg cos T C. Tsin

2 grv

D. Ttan2 grv

E. r

mvN 2

sin T

19. (00)

A student performing a centripetal force experiment whirls a rubber bung attached to one end of a string which

passes through a glass tube with smooth openings, and has a weight W hanging at its other end. The weight of the

rubber bung is much smaller than W. The rubber bung is set into a horizontal uniform circular motion with

angular speed Z while the length of the string beyond the upper opening of the glass tube is L and this portion of the string makes an angle T with the vertical as shown. Which of the following statements is/are correct?

(1) If L is kept constant, T will decrease with Z. (2) If T is kept constant, L will increase with Z. (3) When W increases, T will increase. A. (1) only B. (2) only C. (3) only D. (1) and (2) only E. (2) and (3) only

Q

Pv

Q

P

Q

P

Q

P

Q

P

Q

P

mg

N

r

T

glass

tube

W

TL

rubber

bung

Z

Out of syllabus

MC Question


20. (02)

A particle P is moving in a horizontal circle in a clockwise direction as shown (top view). The following

diagrams show the direction of the acceleration a*

of the particle. Which of them is/are possible?

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

21. (03)

A simple pendulum is pulled horizontal and then released from rest with the string taut. Which of the following

statements about the tension in the string is not correct when the pendulum reaches its vertical position?

A. The tension equals the weight of the pendulum bob in magnitude.

B. The tension attains its greatest value.

C. The tension does not depend on the length of the pendulum.

D. The tension depends on the mass of the pendulum bob.

22 (04)

Suppose a looping the loop experiment is performed on the moon, where the gravitational field strength is 1.6

Nkg-1 on its surface. If the radius of the circular loop is 0.5 m, find the minimum speed v to launch the ball at the

lowest point of the smooth track so that it can complete looping without leaving the track.

A. 0.9 ms-1

B. 1.8 ms-1

C. 2.0 ms-1

D. 4.0 ms-1

1.C 2.A 3.B 4.D 5.B 6.E 7.C 8.D 9.C 10.A 11.A 12.C 13.E 14.A 15.C

16.E 17.A 18.A 19.C 20.C 21.A 22.C

P

P

P

(1) (2) (3)

pendulum in

horizontal position

ball

v

0.5 m

Out of syllabus

Out of syllabus

Out of syllabus

MC Question

Chapter 10Gravitation (MC)10P1

1. (80)

Two identical spheres, each of mass m and radius r are in contact. One sphere is displaced by a distance 4r, along

the line of centres, away from the first sphere. What is the ratio of the original gravitational force between the

spheres to the final gravitational force between them?

A. 3 : 1 B. 9 : 1 C. 16 : 1 D. 25 : 1 E. 36 : 1

2. (81)

The moon orbits the earth once every 27.3 days, with a mean orbital radius of R. What is the period of an earth

satellite with an orbital radius of R/30 ?

A. 4 hr B. 22 hr C. 68 hr D. 260 days E. 4500 days

3. (81)

An astronaut in an orbiting satellite is sometimes said to be weightless. This condition occurs when

(1) the gravitational attraction between the astronaut and the earth is just sufficient to provide the

centripetal force which keeps him in orbit.

(2) there is no reaction of the floor of the satellite on the astronauts feet.

(3) the gravitational pull of the earth is exactly cancelled by the gravitational pull of the moon.


4. (82)

A communication satellite in a circular orbit of radius R has a period of 24 hours. The period of a satellite in a

circular orbit of radius R/4 is

A. 3 hours B. 6 hours C. 12 hours D. 24 hours E. 96 hours

5. (84)

Taking the Earth to be a perfect sphere of uniform density rotating about its polar axis, which of the following

statements concerning the observed acceleration due to gravity, g, at the surface of the Earth is NOT true ?

(1) g at the equator is smaller than that at the poles.

(2) If the rate of rotation of the Earth slows down, g at the equator increases.

(3) If the radius of the Earth increases with its density remaining unchanged, g at the poles decreases.


6. (85)

If v1 is the minimum speed for a projectile to escape from the earth and v2 is the orbital speed of a satellite circling

close to the earth, then v1 / v2 =

A. 2/1 . B. 1 /2. C. 1. D. 2 . E. 2.

7. (87)

A space capsule is launched with speed u from the surface of the Earth to a maximum height above the ground

equal to the radius of the Earth. A rocket is then fired horizontally which keeps the space capsule revolving in a

circular orbit round the earth at that altitude with speed v. The ratio u: v is equal to

A. 1 : 2 B. 1 : 2 C. 1 : 1 D. 2 : 1 E. 2 : 1

8. (88)

A body is suspended by a string and allowed to swing as a simple pendulum. When it is moved from the north

pole to the equator, its period will

A. remain constant.

B. decrease.

C. increase.

D. decrease and then increase.

E. increase and then decrease.

Out of syllabus

Out of syllabus

Out of syllabus

Out of syllabus

MC Question


9. (88)

A satellite moving round the Earth in a circular orbit of radius R has a period T. What would the period be if the

orbit were of radius R/4 ?

A. T/8 B. T/4 C. T/2 D. 2T E. 4T

10. (89)

Two points X and Y are at distances a and 2a from the centre of the Earth as shown in the diagram. The

gravitational potential at X is - 8 kJ kg-1. When a 1 kg mass is taken from X to Y, the work done on the mass is

A. - 4 kJ. B. - 2 kJ. C. + 2 kJ. D. + 4 kJ. E. + 8 kJ.

11. (89)

Assuming the Earth to be a perfect sphere, what would its angular velocity of rotation have to be for an object at

the equator to be weightless (i.e. to give a spring balance reading of zero) ?

(Radius of the Earth = 6.4 u 106 m.) A. 2.4 u 10-12 rad s-1 B. 1.6 u 10-6 rad s-1 C. 1.3 u 10-3 rad s-1 D. 8.0 u 102 rad s-1 E. 6.4 u 105 rad s-1

12. (91)

In which of the following situations is the magnitude of the normal reaction of the supporting surface, R, equal to

the weight of the body, mg?

(1) At rest on a rough inclined plane.

(2) On the floor of a spacecraft in circular orbit around the earth.

(3) On the floor of a lift moving upwards with uniform velocity.


13. (92)

An object of mass m is released from a spacecraft at a distance 3R from the centre of the Earth which has radius R

and mass M. On reaching the Earth's surface, the increase in kinetic energy of the object is

A. GmM / (3R) B. 2GmM / (3R) C. GmM / (2R) D. GmM / R E. 2GmM / R

14. (93)

The period of a simple pendulum undergoing simple harmonic motion may be increased by

A. using a heavier pendulum bob.

B. increasing the amplitude of oscillation.

C. placing the pendulum at the top of a mountain.

D. placing the pendulum at the North Pole.

E. shortening the string attached to the bob.

15. (93)

A communication satellite appears stationary vertically above an observer at the equator. The height of the

satellite above the observer is 3.6 u 107 m. Calculate the mass of the earth. Given : Radius of the earth = 6.4 u 106 m

Gravitational constant = 6.7 u 10-11 N m2 kg-2 A. 4.5 u 1024 kg B. 5.0 u 1024 kg C. 5.5 u 1024 kg D. 6.0 u 1024 kg E. 6.5 u 1024 kg

Out of syllabus

Out of syllabus

Out of syllabus

MC Question


16. (93)

For planets or satellites in circular orbits around a celestial body such as the sun or the earth, the period T is

related to the radius of orbit r by Kepler's 3rd Law T2 = k r3 where k is a constant.

Which of the following statements concerning the constant k is correct?

A. It is a dimensionless constant whose value is not affected by the choice of units.

B. It is a universal constant whose value is not affected by the choice of units.

C. 1t is a universal constant whose value depends on the choice of units.

D. It would have a certain value for the earth moving around the sun, but a different value for another planet

moving around the sun.

E. 1t would have a certain value for all planets moving around the sun, but a different value for all satellites

moving around the earth.

17. (93)

The velocity of escape from the earth is Vo. For a planet with radius twice that of the earth and with density three

times that of the earth, the velocity of escape from the planet would be

A. 3 Vo / 2 B. 2 Vo C. 6 Vo D. 2 3 Vo E. 2 6 Vo

18. (94)

Two satellites A and B of the same mass are moving in circular orbits round the earth. The radius of A's orbit is r

and that of B's orbit is 2 r. Their total mechanical energies are EA and EB respectively. Which of the following

descriptions about EA and EB is correct?

(Gravitational potential energy is taken to be zero at infinity.)

A. EA > 0 and EB = 2EA

B. EA > 0 and EB = EA/ 2

C. EA > 0 and EB = -2EA

D. EA < 0 and EB = 2EA

E. EA < 0 and EB = EA/ 2

19. (95)

On a certain planet, an object is thrown vertically upwards with an initial velocity of v1 and it returns to the

ground after time t. If the velocity of escape from the planet is v2, find the radius of the planet.

A. 2

2

12

v

tv B.

2

2

14

v

tv C.

1

2

22

v

tv D.

1

2

2

4v

tv E.

1

2

2

2v

tv

20. (96)

In which of the following cases is/are the resultant force on the object zero?

(1) a satellite moving round the earth

(2) a feather falling freely in a vacuum cylinder in a laboratory

(3) a gas bubble rising with terminal velocity in water


21. (96)

Two satellites of the same mass travel around the earth in circular orbits of different radii. The satellite in the orbit

with smaller radius has

A. a greater speed.

B. a longer period.

C. a smaller acceleration towards the earth's centre.

D. a greater angular momentum about the earth's centre.

E. a greater sum of gravitational potential energy and kinetic energy.

22. (97)

A low-altitude satellite near the earth's surface has a speed of 7.90 km s-1. The radius of the earth is about 4 times

that of the moon and the ratio of the average density of the earth to that of the moon is about 5 : 4. The speed of a

low-altitude satellite near the moon's surface would be

A. 1.77 km s-1 B. 2.21 km s-1 C. 2.47 km s-1 D. 3.57 km s-1 E. 4.42 km s-1

Out of syllabus

Out of syllabus

Out of syllabus

MC Question


23. (98)

The mass ratio of the earth and the moon is 81 : l and the earth-moon separation is 3.8 u 108 m. At which position between the earth and the moon is the gravitational potential at a maximum ? (Ignore all other planets.)

A. On the surface of the earth

B. 3.4 u 108 m from the earth C. 1.9 u 108 m from the earth D. 0.4 u 108 m from the earth E. On the surface of the moon

24. (99)

Which of the following statements about a communication satellite in parking orbit above the earth's surface is

incorrect ?

A. It is accelerating towards the centre of the earth at all times.

B. It must be in a circular orbit above the earth's equator.

C. It is always vertically above the same place on the earth's surface.

D. It must be rotating in the same sense and with the same angular speed as the earth.

E. It is at a height where its gravitational potential energy is numerically equal to its kinetic energy.

25. (00)

X and Y are two planets. Each of them has a low-altitude satellite revolving in a circular orbit close to the planet.

If the two satellites are observed to have the same period, then X and Y must have nearly the same

A. mass.

B. average density.

C. radius.

D. acceleration due to gravity at the planet's surface.

E. gravitational potential at the planet's surface.

26. (00)

A student used a simple pendulum to measure acceleration due to gravity at the earth's surface. The experimental

value was found higher than the standard value. Which of the following is a possible reason for this?

A. The effect due to air resistance is not negligible.

B. The stop watch used for the experiment runs too slowly.

C. The length of the string has been taken as the effective length of the pendulum.

D. The experiment has been performed at a place above sea-level.

E. The experiment has been performed at a place below sea-level.

27. (02)

Due to air resistance, changes may occur to a satellite orbiting the earth (assuming nearly circular orbit). Which of

the changes below is incorrect?

A. The total mechanical energy of the satellite will decrease.

B. The angular momentum of the satellite about the earths center will decrease.

C. The linear speed of the satellite will increase.

D. The time needed for the satellite to complete one revolution will increase.

28. (03)

Given that the universal gravitational constant is 6.7 u 10-11 N m2 kg-2 and the radius of the earth is 6.4 u 106 m, what is the average density of the earth?

A. 5.6 u 103 kg m-3 B. 7.3 u 103 kg m-3 C. 2.3 u 104 kg m-3 D. 6.0 u 1024 kg m-3

Out of syllabus

Out of syllabus

Out of syllabus

Out of syllabus

MC Question


29. (03)

A satellite of mass m is launched from the earths surface into an orbit at a height of 3R above the earths surface,

where R is the radius of the earth. What is the gravitational potential energy gained by the satellite during this

process?

A. mgR/3

B. mgR/4

C. 2mgR/3

D. 3mgR/4

30. (04)

A planet has a diameter 2 times that of the earth and a mass 3 times that of the earth. What is the approximate

gravitational field strength, in N kg-1, on the planets surface?

A. 7.5

B. 10

C. 15

D. 30

31. (04)

Long ago, astronomers wanted to find out whether the ring of Saturn is a rigid body or a group of satellites

revolving around Saturn. The linear speeds v of different layers of the ring were measured and how v varies with

the distance r from the centre of Saturn was determined. Which of the following relations between v and r

supports the suggestion that

(1) the ring is a rigid body,

(2) the ring is a group of satellites revolving around Saturn ?

(1) (2)

A. v v r v vr

1

B. v v r v vr

1

C. v v r v vr

1

D. v v r v vr

1

32. (05)

An object of mass 5.0 kg has a weight of 8.2 N on the surface of the moon. The radius of the moon is R. What is

the gravitational field strength in N kg-1, at a point distance 2R from the centre of the moon ? (Assume that the

moon is a sphere of uniform density.)

A 1.6

B. 0.8

C. 0.4

D. 0.2

33. (06)

The earth is at a distance r metres from the centre of the sun. It takes 365 days for the earth to revolve once

around the sun in a circular path. Given that universal gravitational constant G = 6.7 u 10-11 N m2 kg-2, find the mass of the sun in terms of r. (Neglect the effects of other planetary objects.)

A. 1.9 u 10-4 r3 kg B. 5.9 u 10-4 r3 kg C. 1.8 u 104 r3 kg D. 1.2 u 106 r3 kg

Answer

1.B 2.A 3.C 4.A 5.B 6.D 7.D 8.C 9.A 10.D 11.C 12.B 13.B 14.C 15.D

16.E 17.D 18.E 19.D 20.B 21.A 22.A 23.B 24.E 25.B 26.B 27.D 28.A 29.D 30.A

31.B 32.C 33.B

Out of syllabus

Out of syllabus

MC Question

Chapter 25 Wave Propagation (MC)25P1

P Q

AO

Direction of sound wave

1 2 3 4 5 678 9 10 11

1 2 3 4 5 6 7 8 9 10 11

Figure (a)

Figure (b)

1. (80)

Which of the following gives typical orders of magnitude of the wavelengths in metres of

(1) infra-red

(2) ultra-violet rays

(3) medium-wave radio waves and

(4) gamma radiation

(1) (2) (3) (4)

A. 102 10-4 10-2 10-7

B. 10-4 10-7 10-2 10-7

C. 10-4 10-7 10-2 10-12

D. 10-7 10-4 102 10-12

E. 10-4 10-7 102 10-12

2. (88)

A loudspeaker at O produces a progressive sound wave of frequency 330 Hz which propagates along OA with a

speed of 330 m s-1. The phase difference between the air vibrations at P and Q, 0.5 m apart, is

A. dependent on the distance OP.

B. zero.

C. 0.5 radians.

D. S / 2 radians. E. S radians.

3. (90)

A rubber band is of unstretched length " and force constant k. When it is stretched to a length 2 ", the speed of transverse waves on it is v. What will be the speed of transverse waves when it is stretched to a length 3 "?

A. v B. v2 C. 3v /2 D. v3 E. 2v

4. (92)

Figure (a) shows the positions of equally spaced molecules in a solid lattice. A longitudinal sound wave travels

from left to right through the solid. At a certain instant, the displaced positions of the molecules are shown in

Figure (b). Immediately afterwards, what will be the directions of motion of particle 1 and particle 7 ?

Particle 1 Particle 7

A. to the right to the right

B. to the right to the left

C. to the left to the right

D. to the left to the left

E. at rest at rest

Out of syllabus

MC Question

Chapter 25 Wave Propagation (MC)25P2

displacement

time in seconds

0 0.20 0.45 0.70

00.3 0.6 0.9

displacement / m

position/m

Figure (a)

00.5 1.5 2.5

displacement / m

time/ms

Figure (b)

direction of propagation of wave

A B

5. (93)

A displacement-time graph of a particle in a plane progressive wave is shown. Wha

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