COM of Discrete Mass Systems — IISER Physics MCQs with Solutions
Free IISER Physics COM of Discrete Mass Systems 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 — COM of Discrete Mass Systems · easy · theory
The centre of mass of a two-particle system always lies:
A. Closer to the lighter one
B. Exactly midway between them
C. Outside the line joining them
D. On the line joining the particles, closer to the heavier one ✓ Correct
Solution: x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂); the mass-weighted average sits nearer the larger mass. Midway only for equal masses.
Q2 — COM of Discrete Mass Systems · medium · theory
The centre of mass of a system of particles:
A. Always lies inside the body
B. Is always at the geometric centre
C. Must lie on one of the particles
D. Need not coincide with any particle of the system ✓ Correct
Solution: E.g. a ring's COM is at its empty centre; an L-shaped lamina's COM can lie outside the material.
Q3 — COM of Discrete Mass Systems · easy · numerical
Masses 2 kg and 3 kg are at x = 0 and x = 5 m. The centre of mass is at x =
A. 3 m ✓ Correct
B. 2.5 m
C. 3.5 m
D. 2 m
Solution: x_cm = (2×0 + 3×5)/5 = 3 m — closer to the 3 kg mass.
Q4 — COM of Discrete Mass Systems · medium · numerical
Three 1 kg masses sit at the corners of an equilateral triangle with side 2 m, one corner at the origin and one side along x. The COM height above the x-axis is:
A. √3/2 m
B. 1 m
C. 1/√3 ≈ 0.58 m ✓ Correct
D. √3 m
Solution: y-coords: 0, 0, √3. y_cm = √3/3 = 1/√3 ≈ 0.58 m (the centroid).
Q5 — COM of Discrete Mass Systems · hard · numerical
Masses 1 kg, 2 kg, 3 kg are at (0,0), (2,0) and (0,2) m. The coordinates of the COM are:
A. (1, 1) m
B. (2/3, 2/3) m
C. (1, 2/3) m
D. (2/3, 1) m ✓ Correct
Solution: x_cm = (0 + 4 + 0)/6 = 2/3; y_cm = (0 + 0 + 6)/6 = 1.
Q6 — COM of Discrete Mass Systems · medium · numerical
Two particles of masses 2 kg and 6 kg are 4 m apart. The COM lies from the 2 kg mass at a distance of:
A. 1.33 m
B. 3 m ✓ Correct
C. 2 m
D. 1 m
Solution: d₁ = m₂D/(m₁+m₂) = 6×4/8 = 3 m — three-quarters of the way towards the heavier mass.
Q7 — COM of Discrete Mass Systems · hard · theory
If all the particles of a system are moved by the SAME displacement d⃗, the centre of mass:
A. Moves by exactly d⃗ ✓ Correct
B. Stays fixed
C. Moves by d⃗/N
D. Moves by N·d⃗
Solution: x_cm is a mass-weighted average of positions; adding d⃗ to every position adds d⃗ to the average — a translation symmetry argument.
Q8 — COM of Discrete Mass Systems · hard · numerical
Masses m and 3m are 8 m apart at rest. To keep the COM fixed, when m is moved 3 m towards 3m, the 3m mass must move:
A. Not at all
B. 1 m away from m ✓ Correct
C. 1 m towards m
D. 3 m away
Solution: mΔx₁ = m×3 (toward) must be balanced: 3m×Δx₂ = 3 ⇒ Δx₂ = 1 m in the opposite sense (away), keeping Σmx constant.