Partially Elastic Collision — JEE Main Physics MCQs with Solutions
Free JEE Main 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 ball is dropped from a height of 32 m onto a horizontal floor. If the coefficient of restitution is 3/4, to what height does the ball rebound?
A. 12 m
B. 16 m
C. 24 m
D. 18 m ✓ Correct
Solution: Rebound height h = e²h₀ = (3/4)² × 32 = (9/16) × 32 = 18 m.
Q2 — Partially Elastic Collision · easy · numerical
A ball dropped from a height of 18 m strikes the ground with coefficient of restitution 1/3. Find the height of the first rebound.
A. 9 m
B. 6 m
C. 2 m ✓ Correct
D. 4 m
Solution: h = e²h₀ = (1/3)² × 18 = 18/9 = 2 m.
Q3 — Partially Elastic Collision · easy · numerical
A ball dropped from a height of 36 m rebounds to a height of 4 m. Find the coefficient of restitution between the ball and the floor.
A. 1/3 ✓ Correct
B. 1/9
C. 2/5
D. 3/4
Solution: e = √(h/h₀) = √(4/36) = 2/6 = 1/3.
Q4 — Partially Elastic Collision · easy · numerical
A 4 kg ball moving at 6 m/s strikes an identical stationary 4 kg ball head-on. If the coefficient of restitution is 1/3, find the velocity of the struck ball after the collision.
A. 6 m/s
B. 3 m/s
C. 4 m/s ✓ Correct
D. 2 m/s
Solution: For equal masses v₂ = (1 + e)u/2 = (4/3) × 6/2 = 4 m/s, and the first ball keeps 2 m/s. Momentum: 4 × 6 = 24 = 4 × 2 + 4 × 4.
Q5 — Partially Elastic Collision · easy · numerical
Two balls moving towards each other with speeds 10 m/s and 6 m/s collide head-on with coefficient of restitution 3/4. Find their speed of separation just after the collision.
A. 12 m/s ✓ Correct
B. 16 m/s
C. 8 m/s
D. 4 m/s
Solution: Separation speed = e × approach speed = (3/4) × (10 + 6) = 12 m/s.
Q6 — Partially Elastic Collision · easy · numerical
Ball A moving at 10 m/s hits an identical stationary ball B head-on. After the collision A moves at 3 m/s and B at 7 m/s along the same line. Find the coefficient of restitution.
A. 3/7
B. 2/5 ✓ Correct
C. 1/3
D. 7/10
Solution: e = (separation)/(approach) = (7 - 3)/(10 - 0) = 4/10 = 2/5. Momentum check: 10 = 3 + 7.
Q7 — Partially Elastic Collision · medium · numerical
A 2 kg ball moving at 24 m/s strikes a stationary 4 kg ball head-on with coefficient of restitution 3/4. Find the velocity of the 2 kg ball after the collision.
A. 4 m/s along its original motion
B. 14 m/s along its original motion
C. 2 m/s opposite to its original motion
D. 4 m/s opposite to its original motion ✓ Correct
Solution: v₁ = (m₁ - em₂)u/(m₁ + m₂) = (2 - 3) × 24/6 = -4 m/s, so it rebounds at 4 m/s while the 4 kg ball moves at 14 m/s. Momentum: 48 = 2 × (-4) + 4 × 14.
Q8 — Partially Elastic Collision · medium · numerical
A 6 kg body moving at 18 m/s strikes a stationary 3 kg body head-on with coefficient of restitution 1/3. Find the velocity of the 6 kg body after the collision.
A. 16 m/s
B. 6 m/s
C. 10 m/s ✓ Correct
D. 12 m/s
Solution: v₁ = (m₁ - em₂)u/(m₁ + m₂) = (6 - 1) × 18/9 = 10 m/s; the 3 kg body moves at 16 m/s. Check: separation 16 - 10 = 6 = (1/3) × 18.
Q9 — Partially Elastic Collision · medium · numerical
A 4 kg body moving at 25 m/s strikes a stationary 6 kg body head-on with coefficient of restitution 2/5. Find the velocity of the 6 kg body after the collision.
A. 10 m/s
B. 14 m/s ✓ Correct
C. 4 m/s
D. 20 m/s
Solution: v₂ = m₁(1 + e)u/(m₁ + m₂) = 4 × (7/5) × 25/10 = 14 m/s; the 4 kg body continues at 4 m/s. Momentum: 100 = 4 × 4 + 6 × 14.
Q10 — Partially Elastic Collision · medium · numerical
A 6 kg ball moving at 12 m/s strikes a stationary 2 kg ball head-on. After the collision the 6 kg ball moves at 8 m/s and the 2 kg ball at 12 m/s, both along the original line. Find the coefficient of restitution.
A. 1/3 ✓ Correct
B. 3/4
C. 2/5
D. 2/3
Solution: e = (12 - 8)/(12 - 0) = 4/12 = 1/3. Momentum check: 6 × 12 = 72 = 6 × 8 + 2 × 12.
Q11 — Partially Elastic Collision · medium · numerical
A 3 kg ball moving at 8 m/s collides head-on with an identical 3 kg ball moving at 4 m/s in the opposite direction; the coefficient of restitution is 1/3. Find the velocity of the first ball (initially at 8 m/s) after the collision.
A. 6 m/s
B. 4 m/s
C. 2 m/s
D. 0 m/s (it comes to rest) ✓ Correct
Solution: The centre of mass moves at (8 - 4)/2 = 2 m/s and the separation speed is (1/3) × 12 = 4 m/s, giving v₁ = 0 and v₂ = 4 m/s reversed. Momentum: 24 - 12 = 12 = 3 × 0 + 3 × 4.
Q12 — Partially Elastic Collision · medium · numerical
A ball is dropped from a height of 81 m onto the floor, with coefficient of restitution 1/3. Find the maximum height reached after the second bounce.
A. 27 m
B. 9 m
C. 3 m
D. 1 m ✓ Correct
Solution: After n bounces h = e²ⁿ h₀, so after two bounces h = (1/9)² × 81 = 1 m (the first bounce reaches 9 m).
Q13 — Partially Elastic Collision · medium · numerical
A ball bounces off a rigid floor with coefficient of restitution 3/4. What fraction of its kinetic energy is lost in one bounce?
A. 9/16
B. 1/4
C. 7/16 ✓ Correct
D. 3/4
Solution: KE after = e² × KE before, so the fraction lost = 1 - e² = 1 - 9/16 = 7/16 (about 44%).
Q14 — Partially Elastic Collision · medium · numerical
A ball hits the ground with coefficient of restitution 2/5. What percentage of its kinetic energy does it retain just after the bounce?
A. 84%
B. 4%
C. 40%
D. 16% ✓ Correct
Solution: Retained fraction = e² = (2/5)² = 4/25 = 16%; the remaining 84% is lost in the impact.
Q15 — Partially Elastic Collision · medium · numerical
A 2 kg ball moving at 9 m/s strikes an identical stationary 2 kg ball head-on with coefficient of restitution 1/3. Find the kinetic energy lost in the collision.
A. 18 J
B. 45 J
C. 36 J ✓ Correct
D. 81 J
Solution: Final velocities are 3 m/s and 6 m/s, so KE falls from 81 J to 9 + 36 = 45 J, a loss of 36 J. This matches ¼(1 - e²)m(Δu)² = ¼ × (8/9) × 2 × 81 = 36 J.
Q16 — Partially Elastic Collision · medium · numerical
A ball strikes a smooth horizontal floor at 45° to the floor, with coefficient of restitution 3/4. Find the tangent of the angle the rebound velocity makes with the floor.
A. 3/4 ✓ Correct
B. 1
C. 3/5
D. 4/3
Solution: The horizontal component is unchanged while the vertical component becomes e times, so tan θ = e tan 45° = 3/4.
Q17 — Partially Elastic Collision · medium · numerical
A 2 kg ball is dropped from a height of 5 m onto the floor; the coefficient of restitution is 2/5. Take g = 10 m/s². Find the magnitude of the impulse given to the ball by the floor.
A. 12 N·s
B. 20 N·s
C. 8 N·s
D. 28 N·s ✓ Correct
Solution: It lands at √(2 × 10 × 5) = 10 m/s and rebounds at (2/5) × 10 = 4 m/s, so the impulse = m(v + v′) = 2 × (10 + 4) = 28 N·s.
Q18 — Partially Elastic Collision · medium · numerical
A ball dropped from a height of 48 m rebounds to a height of 27 m. Find the coefficient of restitution.
A. 1/3
B. 9/16
C. 3/4 ✓ Correct
D. 2/5
Solution: e = √(h/h₀) = √(27/48) = √(9/16) = 3/4.
Q19 — Partially Elastic Collision · medium · numerical
A ball is dropped from a height of 20 m onto the ground; the coefficient of restitution is 2/5. Take g = 10 m/s². Find the speed of the ball just after the first bounce.
A. 8 m/s ✓ Correct
B. 5 m/s
C. 20 m/s
D. 12 m/s
Solution: Impact speed = √(2 × 10 × 20) = 20 m/s, so the rebound speed = e × 20 = (2/5) × 20 = 8 m/s.
Q20 — Partially Elastic Collision · medium · numerical
A ball is dropped from a height of 45 m; the coefficient of restitution with the floor is 1/3. Take g = 10 m/s². How long after the first bounce does the ball reach its highest point?
A. 1 s ✓ Correct
B. 3 s
C. 0.5 s
D. 2 s
Solution: It hits the floor at √(2 × 10 × 45) = 30 m/s and rebounds at 10 m/s, so the time to the top is v/g = 10/10 = 1 s.