# Physics Questions and Answers – Collision

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This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Collision”.

1. What is the coefficient of restitution (e)?
a) Ratio of final to initial relative velocities
b) Ratio of initial to final relative velocities
c) Ratio of final to initial velocity of a body
d) Product of initial to final relative velocities

Explanation: The coefficient of restitution (e) is the ratio of the final to initial relative velocities in a collision system. If the value of e = 1, then the collision is perfectly elastic. If it is equal to 0, then the collision is perfectly inelastic.

2. For what value of e is a collision perfectly elastic?
a) 1
b) 2
c) 0.5
d) 0

Explanation: A perfectly elastic collision occurs when the value of e is 1. When the value of e is less than one the collision starts to becomes inelastic.

3. For what value of e is a collision perfectly inelastic?
a) 1
b) 2
c) 0.5
d) 0

Explanation: A perfectly inelastic collision occurs when the value of e is 0. When the value of e is more than 0 the collision starts to becomes elastic.
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4. For what value of e is a collision partially elastic?
a) 0 < e < 1
b) 1
c) e > 1
d) 0

Explanation: Partially elastic collision occurs when the value of e is less than one and more than zero. In this case the collision is neither perfectly elastic nor perfectly inelastic. Hence, we call it partially elastic collision.

5. A ball of mass 100 g is moving with a velocity of 3 m/s towards east. A cube of mass 200 gram is moving towards west with a velocity of 7 m/s. If the collision is perfectly elastic, what is the magnitude of the final momentum of the system in Kg-m/s?
a) 1700
b) 1500
c) 1300
d) 1100

Explanation: The initial momentum of the system = momentum of ball + momentum of cube = 1100 Kg-m/s. Since the momentum is conserved, the initial momentum = final momentum. Hence the final momentum is 1100 Kg-m/s.
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6. A ball of mass 100 g is moving with a velocity of 3 m/s towards east. A cube of mass 200 gram is moving towards west with a velocity of 7 m/s. If the collision is perfectly elastic, what is the final velocity of the cube in m/s?
a) 7
b) 5
c) 3
d) 11

Explanation: The initial momentum of the system = momentum of ball + momentum of cube = 1100 Kg-m/s eastwards. Since the momentum is conserved, the initial momentum = final momentum. Hence the final momentum is 1100 Kg-m/s eastwards. The collision is perfectly elastic, therefore, e = 1. Therefore, final relative velocity (of cube with respect to ball) = initial relative velocity (of cube with respect to ball). Difference in the final velocities of cube and ball = 4 m/s. From this information and the conservation of momentum, one can find the final velocity of the cube.

7. A ball of mass 100 g is moving with a velocity of 3 m/s towards east. A cube of mass 200 gram is moving towards west with a velocity of 7 m/s. If the collision is perfectly elastic, what is the final velocity of the ball in m/s?
a) 7
b) 5
c) 31/3
d) 11/3

Explanation: The initial momentum of the system = momentum of ball + momentum of cube = 1100 Kg-m/s eastwards. Since the momentum is conserved, the initial momentum = final momentum. Hence the final momentum is 1100 Kg-m/s eastwards. The collision is perfectly elastic, therefore, e = 1. Therefore, final relative velocity (of cube with respect to ball) = initial relative velocity (of cube with respect to ball). Sum of the final velocities of cube and ball = 10 m/s. From this information and the conservation of momentum, one can find the final velocity of the ball.

8. A car of mass 1ton is moving with a velocity of 25 m/s towards left. A truck of mass 5 ton is moving towards left with a velocity of 3 m/s. If the collision is perfectly elastic, what is the final velocity of the truck in m/s?
a) 11
b) 25
c) 3
d) 10

Explanation: The initial momentum of the system = momentum of car + momentum of truck = 40 Kg-m/s leftwards. Since the momentum is conserved, the initial momentum = final momentum. Hence the final momentum is 40 Kg-m/s leftwards. The collision is perfectly elastic, therefore, e = 1. Therefore, final relative velocity (of truck with respect to car) = initial relative velocity (of truck with respect to car). Sum of the final velocities of the car and the truck = 4 m/s. From this information and the conservation of momentum, one can find the final velocity of the truck.

9. When two same masses travelling in opposite directions with different velocities collide perfectly elastically, their velocities ______
a) Exchange
b) Remain unchanged
c) Increase
d) Decrease

Explanation: In this case also we need to conserve the momentum and write the expression for e. After doing so we will find that the sum of the initial velocities is equal to the sum of the final velocities. Same goes for the difference (with slight alterations). This will result in the final velocity of one body being equal to the initial velocity of the other. Hence, the velocities will get exchanged.

10. A ball traveling with some velocity v hits another ball elastically which is stationary. What will happen to the system?
a) The stationary ball will start moving with a velocity v and the moving ball will come at rest
b) The stationary ball remains at rest and the moving ball starts moving in opposite direction
c) Both the balls become stationary
d) Both the balls start moving

Explanation: In this case also we need to conserve the momentum and write the expression for e. After some calculation we will find that the stationary ball will start moving with a velocity v and the moving ball will come at rest.

11. When e < 1, the kinetic energy in the collision is ____
a) Lost
b) Gained
c) Gained exponentially
d) Unchanged

Explanation: Coefficient of restitution or e can be understood as the measure of how much kinetic energy is remaining after the collision. As e becomes lesser and lesser, more kinetic energy is lost in the collision. This can be easily understood with by deriving the coefficient of restitution in a completely elastic collision.

12. Two bodies collide perfectly inelastically, they will ______
a) Move together
b) Move in opposite directions
c) Move separately
d) Remain stationary

Explanation: In complete inelastic motion, the e value is 0. Hence there is not relative motion between he two bodies. Therefore, the two bodies move together as a single body.

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