Elastic Collision — JEE Main Physics MCQs with Solutions
Free JEE Main Physics 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 — Elastic Collision · easy · numerical
A 6 kg sphere moving at 9 m/s makes a head-on elastic collision with a stationary 3 kg sphere. Find the speed of the 3 kg sphere just after the collision.
A. 12 m/s ✓ Correct
B. 9 m/s
C. 6 m/s
D. 3 m/s
Solution: For an elastic collision on a stationary target, v₂ = 2m₁u/(m₁ + m₂) = 2 × 6 × 9 / 9 = 12 m/s. Momentum check: 6 × 9 = 54 = 6 × 3 + 3 × 12.
Q2 — Elastic Collision · easy · numerical
An 8 kg block moving at 5 m/s collides head-on elastically with a stationary 2 kg block. Find the velocity of the 8 kg block after the collision.
A. 5 m/s
B. 8 m/s
C. 2 m/s
D. 3 m/s ✓ Correct
Solution: v₁ = (m₁ - m₂)u/(m₁ + m₂) = (8 - 2) × 5 / 10 = 3 m/s in the original direction; the 2 kg block moves off at 8 m/s.
Q3 — Elastic Collision · easy · numerical
A 5 kg ball moving at 6 m/s strikes a stationary 10 kg block head-on in a perfectly elastic collision. Find the speed of the 10 kg block after the collision.
A. 3 m/s
B. 4 m/s ✓ Correct
C. 2 m/s
D. 6 m/s
Solution: v₂ = 2m₁u/(m₁ + m₂) = 2 × 5 × 6 / 15 = 4 m/s, while the 5 kg ball rebounds at 2 m/s. Momentum: 5 × 6 = 30 = 5 × (-2) + 10 × 4.
Q4 — Elastic Collision · easy · numerical
A ball moves at 12 m/s towards a very massive wall that is itself moving towards the ball at 3 m/s. If the collision is perfectly elastic, find the speed of the ball after it bounces off.
A. 12 m/s
B. 15 m/s
C. 18 m/s ✓ Correct
D. 21 m/s
Solution: Relative to the wall the ball approaches at 12 + 3 = 15 m/s and leaves at 15 m/s, so in the ground frame its speed is 15 + 3 = 18 m/s (equivalently u + 2V = 12 + 2 × 3).
Q5 — Elastic Collision · easy · numerical
Ball A moving at 10 m/s strikes an identical stationary ball B head-on elastically; B then strikes an identical stationary ball C head-on elastically. Find the final speed of ball C.
A. 5 m/s
B. 0 m/s
C. 20 m/s
D. 10 m/s ✓ Correct
Solution: In an elastic collision between equal masses the velocities are exchanged: A stops and B moves at 10 m/s, then B stops and C moves at 10 m/s.
Q6 — Elastic Collision · easy · numerical
Two identical 3 kg balls move towards each other with speeds 10 m/s and 4 m/s and collide head-on elastically. Find the speed, after the collision, of the ball that was moving at 4 m/s.
A. 4 m/s
B. 7 m/s
C. 10 m/s ✓ Correct
D. 6 m/s
Solution: Equal masses exchange velocities in a head-on elastic collision, so the 4 m/s ball moves off at 10 m/s (and the other at 4 m/s). Momentum: 3 × 10 - 3 × 4 = 3 × 10 - 3 × 4.
Q7 — Elastic Collision · medium · numerical
A 2 kg ball moving at 12 m/s collides head-on elastically with a 4 kg ball moving at 3 m/s in the opposite direction. Find the velocity of the 4 kg ball after the collision.
A. 5 m/s
B. 3 m/s
C. 8 m/s
D. 7 m/s ✓ Correct
Solution: v₂ = [(m₂ - m₁)u₂ + 2m₁u₁]/(m₁ + m₂) = [(4 - 2)(-3) + 2 × 2 × 12]/6 = 42/6 = 7 m/s; the 2 kg ball rebounds at 8 m/s. Momentum: 24 - 12 = -16 + 28 = 12.
Q8 — Elastic Collision · medium · numerical
A 4 kg body moving at 9 m/s meets a 2 kg body moving at 6 m/s in the opposite direction; the head-on collision is perfectly elastic. Find the speed of the 2 kg body after the collision.
A. 10 m/s
B. 14 m/s ✓ Correct
C. 8 m/s
D. 12 m/s
Solution: v₂ = [(2 - 4)(-6) + 2 × 4 × 9]/6 = (12 + 72)/6 = 14 m/s; the 4 kg body is left moving at 1 m/s backwards. Momentum: 36 - 12 = -4 + 28 = 24.
Q9 — Elastic Collision · medium · numerical
A 6 kg block moving at 10 m/s catches up with a 2 kg block moving at 2 m/s in the same direction and collides elastically. Find the velocity of the 6 kg block after the collision.
A. 10 m/s
B. 6 m/s ✓ Correct
C. 8 m/s
D. 4 m/s
Solution: v₁ = [(6 - 2) × 10 + 2 × 2 × 2]/8 = 48/8 = 6 m/s, while the 2 kg block speeds up to 14 m/s. Momentum: 60 + 4 = 36 + 28 = 64.
Q10 — Elastic Collision · medium · numerical
A 2 kg ball moving at some speed strikes a stationary 6 kg ball head-on in a perfectly elastic collision. What percentage of the kinetic energy of the 2 kg ball is transferred to the 6 kg ball?
A. 50%
B. 100%
C. 75% ✓ Correct
D. 25%
Solution: Fraction transferred = 4m₁m₂/(m₁ + m₂)² = 4 × 2 × 6 / 8² = 48/64 = 3/4, i.e. 75% of the incident kinetic energy.
Q11 — Elastic Collision · medium · numerical
A fast neutron (mass 1 u) makes a head-on elastic collision with a stationary deuteron (mass 2 u). What fraction of the kinetic energy of the neutron is transferred to the deuteron?
A. 1/2
B. 1/9
C. 8/9 ✓ Correct
D. 16/25
Solution: Fraction transferred = 4mM/(m + M)² = 4 × 1 × 2 / 3² = 8/9 (about 89%), which is why light nuclei make good moderators.
Q12 — Elastic Collision · medium · numerical
A neutron (mass 1 u) collides head-on elastically with a stationary alpha particle (mass 4 u). What fraction of the neutron kinetic energy is transferred to the alpha particle?
A. 8/9
B. 9/25
C. 16/25 ✓ Correct
D. 3/4
Solution: Fraction transferred = 4mM/(m + M)² = 4 × 1 × 4 / 5² = 16/25, i.e. 64% of the neutron energy goes to the alpha particle.
Q13 — Elastic Collision · medium · numerical
A 2 kg block sliding at 15 m/s on a frictionless table hits the spring attached to a stationary 10 kg block. The spring returns all the stored energy, so the collision is perfectly elastic. Find the final speed of the 10 kg block.
A. 10 m/s
B. 15 m/s
C. 2.5 m/s
D. 5 m/s ✓ Correct
Solution: v₂ = 2m₁u/(m₁ + m₂) = 2 × 2 × 15 / 12 = 5 m/s; the 2 kg block rebounds at 10 m/s. Momentum: 2 × 15 = 30 = 2 × (-10) + 10 × 5.
Q14 — Elastic Collision · medium · numerical
A ball moving at 20 m/s strikes an identical stationary ball obliquely in a perfectly elastic, smooth collision. After the collision the struck ball moves at 60° to the original line of motion. Find the speed of the struck ball.
A. 5 m/s
B. 10√3 m/s
C. 10 m/s ✓ Correct
D. 20 m/s
Solution: For an oblique elastic collision between equal masses the two final velocities are perpendicular, so the struck ball has speed u cos 60° = 20 × ½ = 10 m/s (the incident ball moves at 30° with 10√3 m/s).
Q15 — Elastic Collision · medium · numerical
A ball moving at 15 m/s chases a very massive wall that is receding at 3 m/s and hits it head-on elastically. Find the speed of the ball after the bounce.
A. 12 m/s
B. 9 m/s ✓ Correct
C. 15 m/s
D. 21 m/s
Solution: The approach speed relative to the wall is 15 - 3 = 12 m/s; after an elastic bounce the ball leaves the wall at 12 m/s, giving a ground-frame speed of 12 - 3 = 9 m/s (u - 2V = 15 - 6).
Q16 — Elastic Collision · medium · numerical
A 10 kg block moving at 6 m/s makes a head-on elastic collision with a stationary 5 kg block. Find the kinetic energy of the 5 kg block after the collision.
A. 160 J ✓ Correct
B. 80 J
C. 120 J
D. 180 J
Solution: v₂ = 2 × 10 × 6 / 15 = 8 m/s, so KE = ½ × 5 × 8² = 160 J (the 10 kg block continues at 2 m/s, and 20 + 160 = 180 J is conserved).
Q17 — Elastic Collision · medium · numerical
A 4 kg body moving at 12 m/s catches up with an 8 kg body moving at 3 m/s in the same direction and collides head-on elastically. Find the velocity of the 8 kg body after the collision.
A. 12 m/s
B. 9 m/s ✓ Correct
C. 7.5 m/s
D. 6 m/s
Solution: v₂ = [(8 - 4) × 3 + 2 × 4 × 12]/12 = 108/12 = 9 m/s; the 4 kg body comes exactly to rest. Momentum: 48 + 24 = 72 = 8 × 9.
Q18 — Elastic Collision · medium · numerical
A 7 kg ball moving at 6 m/s strikes a stationary ball of mass m head-on in a perfectly elastic collision. For what value of m is the entire kinetic energy of the 7 kg ball transferred to the target?
A. 21 kg
B. 14 kg
C. 7 kg ✓ Correct
D. 3.5 kg
Solution: The transferred fraction 4m₁m₂/(m₁ + m₂)² equals 1 only when m₂ = m₁, so m = 7 kg — equal masses simply exchange velocities and the incident ball stops.
Q19 — Elastic Collision · medium · numerical
A 6 kg trolley moving at 14 m/s catches up with an 8 kg trolley moving at 7 m/s in the same direction, and the collision is perfectly elastic. Find their speed of separation after the collision.
A. 21 m/s
B. 7 m/s ✓ Correct
C. 14 m/s
D. 3.5 m/s
Solution: For e = 1 the separation speed equals the approach speed: 14 - 7 = 7 m/s. (The full solution gives final velocities 6 m/s and 13 m/s, and 13 - 6 = 7.)
Q20 — Elastic Collision · medium · numerical
A 0.5 kg ball moving at 20 m/s hits a rigid fixed wall normally and rebounds elastically. Find the magnitude of the impulse delivered to the wall.
A. 5 N·s
B. 40 N·s
C. 10 N·s
D. 20 N·s ✓ Correct
Solution: The ball rebounds at 20 m/s, so its momentum change is m(v + v) = 0.5 × (20 + 20) = 20 N·s; by Newton third law the wall receives an equal impulse.