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Centre of Mass, Momentum & Collisions — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Centre of Mass, Momentum & Collisions MCQs with step-by-step solutions covering COM of Discrete Mass Systems, COM of Continuous Bodies, COM of Cavity & Truncated Bodies, Motion of COM & Reference Frames, Conservation of Linear Momentum, Impulse & Impulse-Momentum Theorem. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — COM of Discrete Mass Systems · easy · numerical
The separation of H and Cl in an HCl molecule is r; Cl is ~35.5 times heavier than H. The COM lies:
A. Very close to H
B. Outside the molecule
C. At the middle
D. Very close to the Cl atom (≈ r/36.5 from Cl) ✓ Correct
Solution: x from Cl = m_H r/(m_H + m_Cl) = r/36.5 — practically on the chlorine atom.
Q2 — COM of Continuous Bodies · easy · numerical
The centre of mass of a uniform circular RING lies:
A. At its geometric centre, where there is no mass ✓ Correct
B. On the rim
C. R/2 above the centre
D. At 2R/π from the centre
Solution: By symmetry the COM is the centre — an empty point, showing the COM need not lie within the material.
Q3 — COM of Cavity & Truncated Bodies · easy · numerical
A uniform metre stick is cut at the 40 cm mark and the shorter piece is discarded. The COM of the remaining 60 cm piece (from its own left end at 40 cm) is at the stick mark:
A. 75 cm
B. 60 cm
C. 70 cm ✓ Correct
D. 80 cm
Solution: The 60 cm piece spans 40–100 cm; its midpoint is at 70 cm.
Q4 — Motion of COM & Reference Frames · easy · numerical
Two skaters, 40 kg and 60 kg, at rest push off each other on smooth ice. Their centre of mass:
A. Remains at rest where it was ✓ Correct
B. Moves towards the lighter skater
C. Oscillates
D. Moves towards the heavier skater
Solution: The pushes are internal; with no net external horizontal force, v_cm stays zero.
Q5 — Conservation of Linear Momentum · easy · numerical
A 100 kg gun fires a 1 kg shell at 200 m/s. The gun's recoil speed is:
A. 2 m/s ✓ Correct
B. 20 m/s
C. 0.2 m/s
D. 4 m/s
Solution: v = 1×200/100 = 2 m/s.
Q6 — Impulse & Impulse-Momentum Theorem · easy · numerical
A 60 kg athlete lands from a jump and stops his 6 m/s fall in 0.3 s by bending his knees. The average force on him is:
A. 360 N
B. 3600 N
C. 1200 N ✓ Correct
D. 120 N
Solution: F = Δp/t = 60×6/0.3 = 1200 N (plus his weight, if asked for the ground reaction).
Q7 — Elastic Collisions (1D & 2D) · easy · numerical
A moving ball strikes an identical stationary ball elastically but NOT head-on (oblique, smooth). The angle between their final velocities is:
A. 180°
B. 60°
C. 45°
D. 90° ✓ Correct
Solution: For equal masses in an oblique elastic collision the final velocities are perpendicular — a classic result provable from p and KE conservation.
Q8 — Inelastic & Perfectly Inelastic Collisions · easy · numerical
A 3 kg lump of clay at 4 m/s hits a 1 kg block at rest and sticks. The common speed is:
A. 3 m/s ✓ Correct
B. 2 m/s
C. 1 m/s
D. 4 m/s
Solution: v = 12/4 = 3 m/s.
Q9 — Coefficient of Restitution & Rebound · easy · numerical
A ball dropped from 1.8 m rebounds with e = 2/3. The rebound height is:
A. 1.2 m
B. 0.8 m ✓ Correct
C. 0.6 m
D. 0.9 m
Solution: h₁ = e²h = (4/9)×1.8 = 0.8 m.
Q10 — Variable Mass Systems · easy · numerical
Water leaves a fire hose at 20 kg/s with speed 30 m/s. The reaction force on the hose is:
A. 60 N
B. 600 N ✓ Correct
C. 300 N
D. 150 N
Solution: F = v(dm/dt) = 30×20 = 600 N.
Q11 — COM of Discrete Mass Systems · medium · numerical
Masses 1 kg, 2 kg, 3 kg, 4 kg sit at the corners A, B, C, D of a 1 m square (in order). Taking A at the origin with AB along x, x_cm equals:
A. 0.4 m
B. 0.6 m
C. 0.25 m
D. 0.5 m ✓ Correct
Solution: x: A=0, B=1, C=1, D=0 ⇒ x_cm = (0 + 2 + 3 + 0)/10 = 0.5 m.
Q12 — COM of Continuous Bodies · medium · numerical
An L-shaped lamina is made of two identical uniform squares of side 1 m — one at the origin, one directly to its right. The COM of the combination is at:
A. (1, 1) m
B. (1, 0.5) m ✓ Correct
C. (0.5, 0.5) m
D. (0.75, 0.5) m
Solution: Centres: (0.5, 0.5) and (1.5, 0.5), equal masses ⇒ midpoint (1, 0.5).
Q13 — COM of Cavity & Truncated Bodies · medium · numerical
From a disc of radius 6 cm, a hole of radius 2 cm is cut with its centre 3 cm from the disc centre. The COM shift of the remainder is:
A. 1/3 cm
B. 3/8 cm ✓ Correct
C. 3/4 cm
D. 1 cm
Solution: m_hole/M = 4/36 = 1/9; shift = (1/9 × 3)/(8/9) = 3/8 cm away from the hole.
Q14 — Motion of COM & Reference Frames · medium · numerical
A 1 kg and a 2 kg mass start from rest under ONLY their mutual attraction. When the 1 kg mass has speed 2 m/s, the 2 kg mass has speed:
A. 4 m/s
B. 0.5 m/s
C. 2 m/s
D. 1 m/s ✓ Correct
Solution: Momentum stays zero: 1×2 = 2×v ⇒ v = 1 m/s (towards it).
Q15 — Conservation of Linear Momentum · medium · numerical
A 50 kg girl standing on a 150 kg stationary raft (calm water) walks at 2 m/s relative to the WATER. The raft moves at:
A. 1.5 m/s
B. 0.5 m/s
C. 2/3 m/s opposite to her ✓ Correct
D. 2 m/s
Solution: 50×2 = 150×v ⇒ v = 2/3 m/s backwards (total momentum stays zero).
Q16 — Impulse & Impulse-Momentum Theorem · medium · numerical
Rain drops of total mass 0.1 kg/s hit an umbrella at 10 m/s and stop. The extra force on the umbrella is:
A. 10 N
B. 0.1 N
C. 1 N ✓ Correct
D. 100 N
Solution: F = v·dm/dt = 10×0.1 = 1 N — a momentum-flux impulse problem.
Q17 — Elastic Collisions (1D & 2D) · medium · numerical
A 4 kg ball moving at 6 m/s collides elastically head-on with a 2 kg ball at rest. The 2 kg ball moves off at:
A. 4 m/s
B. 12 m/s
C. 8 m/s ✓ Correct
D. 6 m/s
Solution: v₂' = 2m₁u/(m₁+m₂) = (2×4×6)/6 = 8 m/s (the 4 kg ball continues at 2 m/s).
Q18 — Inelastic & Perfectly Inelastic Collisions · medium · numerical
In a perfectly inelastic head-on collision of equal masses (one at rest), the fraction of the initial KE lost is:
A. 1/2 ✓ Correct
B. All of it
C. 1/3
D. 1/4
Solution: v' = u/2 ⇒ KE_f = ½(2m)(u/2)² = mu²/4, while KE_i = mu²/2. So exactly half the kinetic energy is lost.
Q19 — Coefficient of Restitution & Rebound · medium · numerical
A ball dropped from height h keeps bouncing with e = 1/√2. The TOTAL distance travelled before it stops is:
A. 2h
B. 3h ✓ Correct
C. 4h
D. h
Solution: D = h(1 + e²)/(1 − e²) = h(1.5/0.5) = 3h — the classic geometric series.
Q20 — Variable Mass Systems · medium · numerical
A rocket's thrust is 4000 N with exhaust speed 800 m/s. The fuel burn rate is:
A. 5 kg/s ✓ Correct
B. 8 kg/s
C. 2 kg/s
D. 10 kg/s
Solution: dm/dt = F/v_rel = 4000/800 = 5 kg/s.