Motion of COM & Reference Frames — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Motion of COM & Reference Frames 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 — Motion of COM & Reference Frames · easy · theory
The centre of mass of a system accelerates only if:
A. A net EXTERNAL force acts on the system ✓ Correct
B. The system rotates
C. Any internal forces act
D. The particles collide
Solution: M a⃗_cm = F⃗_ext. Internal forces cancel in action–reaction pairs and can never move the COM.
Q2 — Motion of COM & Reference Frames · medium · theory
A shell moving as a projectile explodes in mid-air. The centre of mass of the fragments:
A. Stops instantly
B. Moves straight up
C. Continues along the original parabolic path (until any fragment lands) ✓ Correct
D. Follows a new parabola
Solution: The explosion forces are internal; gravity (external) is unchanged, so the COM keeps its parabola — until a fragment hits the ground and new external forces appear.
Q3 — Motion of COM & Reference Frames · easy · numerical
Two blocks, 2 kg at 6 m/s and 4 kg at 3 m/s, move in the same direction. The velocity of their centre of mass is:
A. 6 m/s
B. 3 m/s
C. 4 m/s ✓ Correct
D. 4.5 m/s
Solution: v_cm = (2×6 + 4×3)/6 = 24/6 = 4 m/s.
Q4 — Motion of COM & Reference Frames · medium · numerical
A 3 kg body moves at +4 m/s and a 2 kg body at −6 m/s (opposite directions). The COM velocity is:
A. +2.4 m/s
B. Zero ✓ Correct
C. −1 m/s
D. +1 m/s
Solution: v_cm = (12 − 12)/5 = 0 — the momenta cancel exactly.
Q5 — Motion of COM & Reference Frames · hard · numerical
A man of mass 60 kg walks 3 m (relative to the boat) towards the shore end of a 120 kg boat on frictionless water. The boat moves back by:
A. 1.5 m
B. 1 m ✓ Correct
C. 2 m
D. 0.75 m
Solution: COM stays fixed: the man moves (3 − x) over the ground while the boat moves x back ⇒ 60(3 − x) = 120x ⇒ x = 1 m. Trap: the man's 3 m is relative to the BOAT, not the ground.
Q6 — Motion of COM & Reference Frames · medium · numerical
In the centre-of-mass (C) frame, the TOTAL linear momentum of a system is:
A. Maximum
B. Equal to Mv_cm
C. Always zero ✓ Correct
D. Conserved only in collisions
Solution: The C-frame is defined as the frame in which Σp⃗ = 0 — the key to quick collision analysis.
Q7 — Motion of COM & Reference Frames · hard · numerical
A projectile at the top of its path (speed 10 m/s, horizontal) explodes into two equal halves; one comes momentarily to rest. The other half's speed just after is:
A. 20 m/s horizontally ✓ Correct
B. 10 m/s
C. 14.1 m/s
D. 5 m/s
Solution: p conserved at the instant: m×10 = (m/2)×0 + (m/2)v ⇒ v = 20 m/s, still horizontal.
Q8 — Motion of COM & Reference Frames · medium · numerical
Two particles, 2 kg at velocity (2î + 2ĵ) and 2 kg at (2î − 2ĵ) m/s: the speed of their COM is:
A. 4 m/s
B. Zero
C. 2√2 m/s
D. 2 m/s ✓ Correct
Solution: v⃗_cm = ½[(2î+2ĵ)+(2î−2ĵ)] = 2î ⇒ 2 m/s along x.