# Momentum and Collisions 27 Multiple Choice Questions

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1. A rocket is fired vertically. At its highest point, it explodes. Which one of the following describes what happens to its total momentum and total kinetic energy as a result of the explosion?

Total momentum Total kinetic energy

A. unchanged increased

B. unchanged unchanged

C. increased increased

D. increased unchanged

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2. Which of the following quantities are conserved in an inelastic collision between two bodies?

Total linear momentum of the bodies Total kinetic energy of the bodies

A. yes yes

B. yes no

C. no yes

D. no no

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3. A ball of mass m falls from rest on to a horizontal plate and bounces off it. The magnitudes of its

velocity just before and just after the bounce are v1 and v2 respectively. The variation with time t

of the velocity v of the ball is shown below.

v v

– v

0

0 t t t t

1

1 2 3

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The magnitude of the net force on the ball is given by which one of the following? A. 1 1 t mv B. ) –

(3 2

2

t t

mv

C.

## 

1 2 2 1 t t v v m  

D.

## 

1 2 2 1 t t v v m   (1)

4. Joe is standing on the surface of a frozen pond and he throws a ball horizontally. Considering

Joe and the ball together, which one of the following correctly describes the change in the magnitude of the momentum and the change in the kinetic energy of Joe and the ball immediately after the ball is thrown?

Magnitude of momentum of Joe and ball Kinetic energy of Joe and ball

A. No change Increases

B. Increases Increases

C. No change No change

D. Increases No change

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5. An astronaut in outer space is holding a hammer and drifting at constant velocity. The astronaut

throws the hammer in the opposite direction to that in which she is drifting.

What change, if any, occurs in the total kinetic energy and the total momentum of the astronaut and hammer?

Total kinetic energy Total momentum

A. unchanged increased

B. unchanged unchanged

C. increased increased

D. increased unchanged

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6. A constant force is applied to a ball of mass m. The velocity of the ball changes from v1 to v2.

The impulse received by the ball is

A. m(v2 + v1).

B. m(v2 – v1).

C. m(v22 + v12).

D. m(v22 – v12).

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7. A ball of mass 2.0 kg falls vertically and hits the ground with speed 7.0 ms–1 as shown below.

7 . 0 m s– 1

– 1

3 . 0 m s

before after

The ball leaves the ground with a vertical speed 3.0 ms–1.

The magnitude of the change in momentum of the ball is

A. zero.

B. 8.0 Ns.

C. 10 Ns.

D. 20 Ns.

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8. Which of the following quantities are conserved in an inelastic collision in an isolated system of two objects?

Linear momentum of system Kinetic energy of system

A. Yes Yes

B. Yes No

C. No Yes

D. No No

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9. A stone on a string is moving in a circle as shown below.

P

Q

v

v

y– d i r e c t i o n

x– d i r e c t i o n

At point P, the stone of mass m has speed v in the y-direction. A quarter of a revolution later, the stone at point Q has speed v in the x-direction.

What is the change, in the y-direction only, of the magnitude of the momentum of the stone?

A. zero

B. mv

C. 2mv

D. 2mv

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10. Two spheres X and Y are moving towards each other along the same straight line with momenta

of magnitude PX and PY respectively. The spheres collide and move off with momenta pX and

pY respectively, as illustrated below.

X Y X Y

Px PY px pY

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Which one of the following is a correct statement of the law of conservation of momentum for this collision?

A. PX + PY = pX + pY

B. PX – PY = pX + pY

C. PX – PY = pX – pY

D. PX + PY = pX – pY

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11. The momentum of a system is conserved if

A. no external forces act on the system.

B. no friction forces act within the system.

C. no kinetic energy is lost or gained by the system.

D. the forces acting on the system are in equilibrium.

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12. The velocity of a body of mass m changes by an amount v in a time t. The impulse given to

the body is equal to

A. mt.

B. .

t v  

C. .

t v m

 

D. mv.

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13. A ball is held at rest at point X and is then released. It drops on to a flat horizontal surface and rebounds to a maximum height at point Y.

p o i n t X

p o i n t Y

b e f o r e a f t e r

Which one of the following graphs best shows the variation with time t of the momentum p of the ball as it moves between point X and point Y?

A . B .

C . D .

p

t

0 0

p

t

0 0

p

t

0 0

p

t

0 0

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14. A small ball P moves with speed v towards another identical ball Q along a line joining the centres of the two balls. Ball Q is at rest. Kinetic energy is conserved in the collision.

P Q a t r e s t

v

Which one of the following situations is a possible outcome of the collision between the balls?

P Q

P Q

P Q

P Q

A . B .

C . D .

v v

v 3 v

4 4

v = 0 v

v v

2 2

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15. Two spheres of masses m1 and m2 are moving towards each other along the same straight-line

with speeds v1 and v2 as shown.

p o s i t i v e d i r e c t i o n

m 1 v1 v2 m 2

The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a result of the collision?

A. 0

B. m1v1 + m2v2

C. m1v1 − m2v2

D. m2v2 − m1v1

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16. An object of mass m is initially at rest. An impulse I acts on the object. The change in kinetic energy of the object is

A.

2

B.

2

### I

C. I2m.

D. 2I2m.

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17. The engine of a rocket ejects gas at high speed, as shown below.

h i g h s p e e d g a s

r o c k e t

d i r e c t i o n o f

m o t i o n o f r o c k e t

The rocket accelerates forwards because

A. the momentum of the gas is equal but opposite in direction to the momentum of the

rocket.

B. the gas pushes on the air at the back of the rocket.

C. the change in momentum of the gas gives rise to a force on the rocket.

D. the ejected gas creates a region of high pressure behind the rocket.

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18. A stationary metal plate is hanging freely on a string. A steel ball, travelling horizontally, hits the plate. The speed of the ball after the collision is less than before, but still in a horizontal direction, as shown below.

b e f o r e c o l l i s i o n

a f t e r c o l l i s i o n

s t r i n g

m e t a l p l a t e

Which one of the following gives a correct statement, with a valid reason, about the type of collision between the ball and the plate?

Type of collision Reason

A. inelastic The sphere has changed its momentum during the collision.

B. inelastic The sphere has lost kinetic energy during the collision.

C. unknown The change in momentum of the plate during the collision is unknown.

D. unknown The kinetic energy of the plate after the collision is unknown.

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19. A fan and a sail are mounted vertically on a cart that is initially at rest on a horizontal table as shown in the diagram below.

f a n a i r

s a i l

When the fan is turned on an air stream is blown towards the right and is incident on the sail. The cart is free to move with negligible resistance forces.

After the fan has been turned on the cart will

A. move to the left and then to the right.

B. remain at rest.

C. move towards the right.

D. move towards the left.

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20. Two objects collide inelastically. For this system of two objects

A. only momentum is conserved.

B. only kinetic energy is conserved.

C. both momentum and kinetic energy are conserved.

D. neither momentum nor kinetic energy are conserved.

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21. A net force of magnitude F acts on a body for a time t producing an impulse of magnitude Y.

Which of the following is the magnitude of the rate of change of momentum of the body?

A. F

B. Ft

C. Y

D. Yt

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22. The diagram below shows a trolley of mass 4.0 kg moving on a frictionless horizontal table with

a speed of 2.0 m s–1. It collides with a stationary trolley also of mass 4.0 kg.

4 . 0 k g 4 . 0 k g

2 . 0 m s– 1

Which of the following diagrams shows a possible outcome?

2 . 0 m s– 1

2 . 0 m s– 1

2 . 0 m s– 1

0 . 0 m s– 1

0 . 0 m s– 1

0 . 0 m s– 1

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g

4 . 0 k g 4 . 0 k g

4 . 0 k g 4 . 0 k g

A . B .

C . D .

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23. A ball of mass M hits a wall at speed V normal to the wall. It rebounds with speed v normal to the wall as shown below.

w a l l

M V

v

l e f t r i g h t

What is the magnitude of the change in momentum of the ball and the direction of the force that the wall exerts on the ball?

change in momentum direction of force

A. M(V – v) to the right

B. M(V – v) to the left

C. M(V + v) to the right

D. M(V + v) to the left

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24. A rocket is fired vertically into the air. When the rocket reaches its maximum height, the rocket

explodes.

What change, if any, occurs in the momentum and in the kinetic energy of the rocket during the explosion?

momentum kinetic energy

A. increases increases

B. increases constant

C. constant increases

D. constant constant

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25. Two trolleys P and Q, are connected by a rubber band. They are at rest on a horizontal surface. The mass of Q is twice that of P. The trolleys are pulled apart so that the band is stretched and are then released.

The ratio Q trolley of on accelerati initial of magnitude P trolley of on accelerati initial of magnitude is A. 4 1 . B. 2 1 . C. 1. D. 2. (1)

26. An impulse I acts on a body of mass m that is initially at rest. What is the distance moved by the

body in a time t after the impulse has been delivered?

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27. Two spheres of masses m1 and m2 are moving towards each other along the same straight-line

with speeds v1 and v2 as shown.

The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a result of the collision?

A. 0

B. m1v1 + m2v2

C. m1v1 − m2v2

D. m2v2 − m1v1

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