Partially Elastic Collision — NEET Physics MCQs with Solutions
Free NEET Physics Partially Elastic Collision MCQs with step-by-step solutions (20 questions). Part of Collision. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Partially Elastic Collision · easy · numerical
A 5 kg ball moving at 8 m/s collides head-on with an identical 5 kg ball at rest. If the coefficient of restitution is 1/2, find the velocity of the second ball after the collision.
A. 8 m/s
B. 6 m/s ✓ Correct
C. 4 m/s
D. 2 m/s
Solution: For equal masses with the target at rest, v₂ = u(1 + e)/2 = 8 × (3/2)/2 = 6 m/s (the first ball moves at 2 m/s; momentum: 40 = 10 + 30).
Q2 — Partially Elastic Collision · easy · numerical
A 3 kg ball moving at 12 m/s strikes an identical 3 kg ball at rest head-on with coefficient of restitution 1/2. What is the velocity of the striking ball after the collision?
A. 3 m/s ✓ Correct
B. 4 m/s
C. 9 m/s
D. 6 m/s
Solution: v₁ = u(1 − e)/2 = 12 × (1/2)/2 = 3 m/s, while the struck ball moves at 9 m/s (momentum: 36 = 9 + 27).
Q3 — Partially Elastic Collision · easy · numerical
A 1 kg ball moving at 8 m/s hits an identical 1 kg ball at rest head-on. If e = 1/4, find the velocity of the struck ball after the collision.
A. 3 m/s
B. 5 m/s ✓ Correct
C. 2 m/s
D. 4 m/s
Solution: v₂ = u(1 + e)/2 = 8 × (5/4)/2 = 5 m/s; the striker keeps v₁ = 8 × (3/4)/2 = 3 m/s (momentum: 8 = 3 + 5).
Q4 — Partially Elastic Collision · easy · numerical
Two bodies approach each other with a relative speed of 8 m/s. After the collision they separate with a relative speed of 2 m/s. What is the coefficient of restitution?
A. 0.75
B. 0.25 ✓ Correct
C. 0.4
D. 0.5
Solution: e = speed of separation / speed of approach = 2/8 = 0.25.
Q5 — Partially Elastic Collision · easy · numerical
A ball dropped from a height of 16 m rebounds to a height of 4 m. Find the coefficient of restitution between the ball and the floor.
A. 1/4
B. 1/16
C. 3/4
D. 1/2 ✓ Correct
Solution: e = √(h′/h) = √(4/16) = 1/2.
Q6 — Partially Elastic Collision · easy · numerical
A ball dropped from a height of 16 m rebounds to a height of only 1 m. What is the coefficient of restitution?
A. 0.25 ✓ Correct
B. 0.0625
C. 0.125
D. 0.5
Solution: e = √(h′/h) = √(1/16) = 1/4.
Q7 — Partially Elastic Collision · easy · numerical
A ball is dropped from a height of 12 m onto a floor. If the coefficient of restitution is 1/2, to what height does it rebound?
A. 4 m
B. 6 m
C. 1.5 m
D. 3 m ✓ Correct
Solution: h′ = e²h = (1/2)² × 12 = 3 m.
Q8 — Partially Elastic Collision · easy · numerical
A ball falls from a height of 32 m onto the ground. If the coefficient of restitution is 1/4, how high does it rise after the first bounce?
A. 8 m
B. 1 m
C. 4 m
D. 2 m ✓ Correct
Solution: h′ = e²h = (1/16) × 32 = 2 m.
Q9 — Partially Elastic Collision · easy · numerical
A ball hits a fixed wall normally at 12 m/s. If the coefficient of restitution is 1/2, with what speed does it rebound?
A. 6 m/s ✓ Correct
B. 12 m/s
C. 3 m/s
D. 9 m/s
Solution: Rebound speed = e × approach speed = (1/2) × 12 = 6 m/s.
Q10 — Partially Elastic Collision · easy · numerical
A ball strikes a rigid floor vertically at 8 m/s. Taking e = 1/4, find the speed with which it leaves the floor.
A. 1 m/s
B. 4 m/s
C. 6 m/s
D. 2 m/s ✓ Correct
Solution: v′ = ev = (1/4) × 8 = 2 m/s.
Q11 — Partially Elastic Collision · easy · numerical
A ball bounces on a floor with coefficient of restitution 1/2. What percentage of its kinetic energy is lost in one bounce?
A. 50%
B. 87.5%
C. 75% ✓ Correct
D. 25%
Solution: Fraction lost = 1 − e² = 1 − 1/4 = 3/4 = 75%.
Q12 — Partially Elastic Collision · easy · numerical
A ball rebounds from a floor with coefficient of restitution 1/4. What percentage of its kinetic energy does it retain after the bounce?
A. 6.25% ✓ Correct
B. 12.5%
C. 25%
D. 93.75%
Solution: Fraction retained = e² = (1/4)² = 1/16 = 6.25%.
Q13 — Partially Elastic Collision · medium · numerical
A ball is dropped from a height of 48 m. If the coefficient of restitution with the floor is 1/2, to what height does it rise after the SECOND bounce?
A. 3 m ✓ Correct
B. 1.5 m
C. 6 m
D. 12 m
Solution: After n bounces h_n = e²ⁿh, so h₂ = (1/2)⁴ × 48 = 48/16 = 3 m (it rises 12 m after the first bounce).
Q14 — Partially Elastic Collision · medium · numerical
A 5 kg ball hits a rigid floor vertically at 4 m/s and rebounds with coefficient of restitution 1/4. What impulse does the floor exert on the ball?
A. 5 N·s
B. 25 N·s ✓ Correct
C. 20 N·s
D. 15 N·s
Solution: Rebound speed = 4 × (1/4) = 1 m/s, so impulse = m(v₁ + v₂) = 5 × (4 + 1) = 25 N·s.
Q15 — Partially Elastic Collision · medium · numerical
A 3 kg ball moving at 6 m/s collides head-on with a 6 kg ball at rest, with coefficient of restitution 1/2. What is the velocity of the 3 kg ball after the collision?
A. It comes to rest ✓ Correct
B. 2 m/s in its original direction
C. 1 m/s opposite to its original direction
D. 3 m/s in its original direction
Solution: v₁ = (m₁ − e·m₂)u/(m₁ + m₂) = (3 − 3) × 6/9 = 0, so the striker stops while the 6 kg ball moves off at 3 m/s (momentum: 18 = 0 + 18).
Q16 — Partially Elastic Collision · medium · numerical
A 5 kg body moving at 7 m/s collides head-on with a 2 kg body at rest. If e = 1/2, find the velocity of the 2 kg body after the collision.
A. 7.5 m/s ✓ Correct
B. 4 m/s
C. 3.5 m/s
D. 10.5 m/s
Solution: v₂ = m₁(1 + e)u/(m₁ + m₂) = 5 × (3/2) × 7/7 = 7.5 m/s; the 5 kg body continues at 4 m/s (momentum: 35 = 20 + 15).
Q17 — Partially Elastic Collision · medium · numerical
A 6 kg ball moving at 12 m/s collides head-on with an identical 6 kg ball at rest, with e = 1/2. How much kinetic energy is lost in the collision?
A. 108 J
B. 270 J
C. 162 J ✓ Correct
D. 216 J
Solution: Final velocities are 3 m/s and 9 m/s, so KE drops from 432 J to 27 + 243 = 270 J, a loss of 162 J (= (1 − e²)/2 of the initial KE).
Q18 — Partially Elastic Collision · medium · numerical
A ball is dropped from a height of 1.25 m onto the ground. If the coefficient of restitution is 1/2, with what speed does it leave the ground after the bounce? (g = 10 m/s²)
A. 1.25 m/s
B. 3.75 m/s
C. 5 m/s
D. 2.5 m/s ✓ Correct
Solution: It lands at v = √(2gh) = √(2 × 10 × 1.25) = 5 m/s and rebounds at ev = (1/2) × 5 = 2.5 m/s.
Q19 — Partially Elastic Collision · medium · numerical
A 2 kg ball strikes a wall normally at 14 m/s and rebounds with coefficient of restitution 1/2. What is the magnitude of the impulse the wall gives the ball?
A. 28 N·s
B. 42 N·s ✓ Correct
C. 14 N·s
D. 56 N·s
Solution: Rebound speed = 14 × (1/2) = 7 m/s, so impulse = m(v₁ + v₂) = 2 × (14 + 7) = 42 N·s.
Q20 — Partially Elastic Collision · medium · numerical
Two balls approach each other head-on with speeds 9 m/s and 3 m/s. After the collision they move apart with a relative speed of 6 m/s. Find the coefficient of restitution.
A. 1/4
B. 3/4
C. 2/3
D. 1/2 ✓ Correct
Solution: Speed of approach = 9 + 3 = 12 m/s, so e = separation/approach = 6/12 = 1/2.