Elastic Collisions (1D & 2D) — IISER Physics MCQs with Solutions
Free IISER Physics Elastic Collisions (1D & 2D) MCQs with step-by-step solutions (8 questions). Part of Centre of Mass, Momentum & Collisions. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Elastic Collisions (1D & 2D) · easy · theory
In a perfectly elastic collision, the quantities conserved are:
A. Neither
B. Only kinetic energy
C. Only momentum
D. Both linear momentum and kinetic energy ✓ Correct
Solution: Elastic: p⃗ and KE both conserved. (Momentum is conserved in ALL collisions; KE only in elastic ones.)
Q2 — Elastic Collisions (1D & 2D) · medium · theory
In a 1D elastic collision between two EQUAL masses (one initially at rest), after the collision:
A. They stick together
B. The mover rebounds
C. They exchange velocities — the mover stops, the target moves off with the original velocity ✓ Correct
D. Both move at half speed
Solution: Equal-mass elastic exchange: v₁' = 0, v₂' = u. Seen in billiards and in neutron moderation by hydrogen.
Q3 — Elastic Collisions (1D & 2D) · easy · numerical
A 2 kg ball at 6 m/s hits an identical stationary ball head-on, perfectly elastically. The speeds after are:
A. 0 and 6 m/s ✓ Correct
B. 3 and 3 m/s
C. 6 and 6 m/s
D. 2 and 4 m/s
Solution: Equal masses exchange velocities: the incoming ball stops; the struck one leaves at 6 m/s.
Q4 — Elastic Collisions (1D & 2D) · medium · numerical
A ball of mass m at speed u strikes a much HEAVIER wall elastically and head-on. It rebounds with speed:
A. u (same speed, reversed) ✓ Correct
B. Zero
C. 2u
D. u/2
Solution: Limit m₂ → ∞: v₁' = −u. The wall barely moves but reverses the ball's momentum.
Q5 — Elastic Collisions (1D & 2D) · hard · numerical
A 2 kg ball at 9 m/s strikes a 1 kg stationary ball elastically head-on. Their final velocities are:
A. 3 m/s and 12 m/s ✓ Correct
B. 4.5 m/s each
C. 6 m/s and 3 m/s
D. 0 and 9 m/s
Solution: v₁' = (m₁−m₂)u/(m₁+m₂) = (1/3)×9 = 3 m/s; v₂' = 2m₁u/(m₁+m₂) = (4/3)×9 = 12 m/s.
Q6 — Elastic Collisions (1D & 2D) · medium · numerical
In an elastic head-on collision, a neutron (mass 1) strikes a carbon nucleus (mass 12) at rest. The fraction of its kinetic energy transferred is:
A. 4/13
B. 100%
C. 48/169 ≈ 28% ✓ Correct
D. 1/12
Solution: Fraction = 4m₁m₂/(m₁+m₂)² = 48/169 ≈ 0.28 — why light moderators (hydrogen) beat carbon.
Q7 — Elastic Collisions (1D & 2D) · hard · theory
In the C-frame, a 1D elastic collision simply:
A. Reverses each particle's velocity while keeping its magnitude ✓ Correct
B. Rotates velocities by 45°
C. Doubles each speed
D. Stops both particles
Solution: With Σp = 0 and KE conserved, the only allowed outcome is v⃗ᵢ → −v⃗ᵢ for each particle — which is why C-frame analysis is so fast.
Q8 — Elastic Collisions (1D & 2D) · hard · numerical
A ball of mass m moving at u hits a stationary ball of mass M elastically head-on. The fraction of KE RETAINED by the projectile is:
A. Always ½
B. [(m − M)/(m + M)]² ✓ Correct
C. 4mM/(m+M)²
D. M/(m+M)
Solution: v₁'/u = (m−M)/(m+M) ⇒ retained fraction is its square; the transferred fraction 4mM/(m+M)² completes it to 1.