Question 1

A 3 kg ball moving at 8 m/s collides head-on elastically with an identical 3 kg ball at rest. What is the velocity of the second ball after the collision?

Accepted Answer

8 m/s. In an elastic collision between equal masses, velocities are exchanged: the first ball stops and the second moves off at 8 m/s.

Question 2

Two identical 4 kg balls move in the same direction at 10 m/s and 4 m/s. The faster ball catches up and collides head-on elastically with the slower one. What is the velocity of the faster ball just after the collision?

Accepted Answer

4 m/s. Equal masses exchange velocities in an elastic collision, so the ball that was moving at 10 m/s now moves at 4 m/s.

Question 3

A 5 kg block moving at 9 m/s collides head-on elastically with another 5 kg block moving at 3 m/s in the same direction. Find the velocity of the slower block after the collision.

Accepted Answer

9 m/s. Equal masses exchange velocities: the slower block moves off at 9 m/s while the other slows to 3 m/s.

Question 4

A 6 kg ball moving at 8 m/s strikes a 2 kg ball at rest in a head-on elastic collision. What is the velocity of the 2 kg ball after the collision?

Accepted Answer

12 m/s. v₂ = 2m₁u₁/(m₁ + m₂) = (2 × 6 × 8)/8 = 12 m/s, while the 6 kg ball continues at 4 m/s (momentum: 48 = 24 + 24).

Question 5

A 3 kg body moving at 4 m/s makes a head-on elastic collision with a 1 kg body at rest. What is the velocity of the 3 kg body after the collision?

Accepted Answer

2 m/s. v₁ = (m₁ − m₂)u₁/(m₁ + m₂) = (3 − 1)(4)/4 = 2 m/s, while the 1 kg body moves off at 6 m/s.

Question 6

A 1 kg ball moving at 6 m/s hits a stationary 2 kg ball in a head-on elastic collision. Find the velocity of the 2 kg ball after impact.

Accepted Answer

4 m/s. v₂ = 2m₁u₁/(m₁ + m₂) = (2 × 1 × 6)/3 = 4 m/s; the 1 kg ball rebounds at 2 m/s (momentum: 6 = −2 + 8).

Question 7

A 2 kg ball moving at 3 m/s collides head-on elastically with a 4 kg ball at rest. With what speed does the 2 kg ball rebound?

Accepted Answer

1 m/s. v₁ = (m₁ − m₂)u₁/(m₁ + m₂) = (2 − 4)(3)/6 = −1 m/s, i.e. it rebounds at 1 m/s while the 4 kg ball moves at 2 m/s.

Question 8

A 1 kg ball moving at 12 m/s collides head-on elastically with a stationary ball that is very much heavier than it. What is the approximate velocity of the 1 kg ball after the collision?

Accepted Answer

≈ 12 m/s, opposite to its initial direction. When m₂ ≫ m₁, v₁ = (m₁ − m₂)u₁/(m₁ + m₂) ≈ −u₁, so the light ball rebounds with nearly its original speed of 12 m/s.

Question 9

A very heavy body moving at 5 m/s collides head-on elastically with a 2 kg ball at rest. What is the approximate speed of the 2 kg ball after the collision?

Accepted Answer

≈ 10 m/s. When m₁ ≫ m₂, v₂ = 2m₁u₁/(m₁ + m₂) ≈ 2u₁ = 2 × 5 = 10 m/s.

Question 10

A 1 kg body moving at 4 m/s makes a head-on elastic collision with a 3 kg body at rest. What fraction of its kinetic energy is transferred to the 3 kg body?

Accepted Answer

75%. Fraction transferred = 4m₁m₂/(m₁ + m₂)² = (4 × 1 × 3)/16 = 3/4 = 75% (the 3 kg body carries 6 J of the initial 8 J).

Question 11

A 2 kg ball moving at 12 m/s strikes a 6 kg ball at rest in a head-on elastic collision. What percentage of its initial kinetic energy does the 2 kg ball retain after the collision?

Accepted Answer

25%. Fraction retained = ((m₁ − m₂)/(m₁ + m₂))² = ((2 − 6)/8)² = 1/4 = 25%; it rebounds at 6 m/s, keeping 36 J of the initial 144 J.

Question 12

Two identical 4 kg balls approach each other with speeds 5 m/s and 3 m/s and collide head-on elastically. What is the velocity of the ball that was moving at 5 m/s after the collision?

Accepted Answer

3 m/s, opposite to its original direction. Equal masses exchange velocities in a head-on elastic collision, so the 5 m/s ball now moves at 3 m/s opposite to its original direction.

Question 13

A 4 kg ball moving at 9 m/s collides with a 2 kg ball at rest and the two stick together. What is their common velocity just after the collision?

Accepted Answer

6 m/s. By momentum conservation, v = m₁u₁/(m₁ + m₂) = (4 × 9)/6 = 6 m/s.

Question 14

A 1 kg body moving at 10 m/s strikes a 4 kg body at rest and embeds in it. Find the velocity of the combined mass.

Accepted Answer

2 m/s. v = m₁u₁/(m₁ + m₂) = (1 × 10)/5 = 2 m/s.

Question 15

A 5 kg block sliding at 12 m/s on a smooth surface hits a 1 kg block at rest and the two move off together. What is their common speed?

Accepted Answer

10 m/s. v = m₁u₁/(m₁ + m₂) = (5 × 12)/6 = 10 m/s.

Question 16

A 3 kg ball moving at 5 m/s collides head-on with a 2 kg ball moving at 5 m/s in the opposite direction. If they stick together, what is the speed of the combined mass?

Accepted Answer

1 m/s. Net momentum = 3 × 5 − 2 × 5 = 5 kg·m/s, so v = 5/(3 + 2) = 1 m/s along the initial direction of the 3 kg ball.

Question 17

A 3 kg trolley moving at 11 m/s catches up with another 3 kg trolley moving at 7 m/s in the same direction and couples with it. Find their common velocity.

Accepted Answer

9 m/s. v = (m₁u₁ + m₂u₂)/(m₁ + m₂) = (33 + 21)/6 = 9 m/s.

Question 18

A 40 g bullet moving at 200 m/s embeds itself in a 1.96 kg block resting on a smooth floor. With what speed does the block (with the bullet) start moving?

Accepted Answer

4 m/s. v = m₁u₁/(m₁ + m₂) = (0.04 × 200)/2.00 = 8/2 = 4 m/s.

Question 19

A 6 kg body moving at 3 m/s collides with a 3 kg body at rest and they stick together. How much kinetic energy is lost in the collision?

Accepted Answer

9 J. v = 18/9 = 2 m/s, so KE loss = ½ × 6 × 3² − ½ × 9 × 2² = 27 − 18 = 9 J.

Question 20

A 2 kg ball moving at 8 m/s strikes a 6 kg ball at rest and the two stick together. What percentage of the initial kinetic energy is lost?

Accepted Answer

75%. v = 16/8 = 2 m/s; KE falls from 64 J to ½ × 8 × 2² = 16 J, so 48/64 = 75% is lost (= m₂/(m₁ + m₂) = 6/8).

Collision — NEET Physics MCQs with Solutions

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