Conservation of Linear Momentum — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Conservation of Linear Momentum 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 — Conservation of Linear Momentum · easy · theory
The total linear momentum of a system is conserved when:
A. The bodies are rigid
B. Gravity is absent
C. Kinetic energy is conserved
D. The net external force on the system is zero ✓ Correct
Solution: dP⃗/dt = F⃗_ext; zero net external force ⇒ P⃗ constant, whatever the internal forces (collisions, explosions).
Q2 — Conservation of Linear Momentum · medium · theory
A bomb at rest explodes into fragments. Immediately afterwards, the vector sum of the momenta of all fragments is:
A. Equal to the energy released
B. Random
C. Zero ✓ Correct
D. Directed upward
Solution: The explosion is internal: total momentum stays what it was — zero. (Kinetic energy, of course, increases.)
Q3 — Conservation of Linear Momentum · easy · numerical
A 40 kg boy on frictionless ice throws a 2 kg ball at 10 m/s. His recoil speed is:
A. 0.05 m/s
B. 0.5 m/s ✓ Correct
C. 2 m/s
D. 5 m/s
Solution: 40v = 2×10 ⇒ v = 0.5 m/s backwards.
Q4 — Conservation of Linear Momentum · medium · numerical
A 10 g bullet is fired at 500 m/s from a 5 kg rifle. The rifle's recoil speed is:
A. 1 m/s ✓ Correct
B. 2 m/s
C. 0.1 m/s
D. 10 m/s
Solution: v = (0.01×500)/5 = 1 m/s. The rifle's KE is far smaller — momentum is shared equally, energy is not.
Q5 — Conservation of Linear Momentum · hard · numerical
A shell at rest explodes into two pieces with mass ratio 1 : 3. The ratio of their kinetic energies (light : heavy) is:
A. 1 : 1
B. 1 : 3
C. 9 : 1
D. 3 : 1 ✓ Correct
Solution: Equal/opposite momenta ⇒ KE = p²/2m ∝ 1/m ⇒ 3:1 — the lighter piece takes the lion's share of energy.
Q6 — Conservation of Linear Momentum · medium · numerical
A 60 kg man jumps with velocity 4 m/s from a stationary 240 kg trolley (free to roll). The trolley recoils at:
A. 4 m/s
B. 1 m/s ✓ Correct
C. 0.5 m/s
D. 2 m/s
Solution: 240v = 60×4 ⇒ v = 1 m/s opposite the jump.
Q7 — Conservation of Linear Momentum · hard · numerical
A 1 kg ball moving at 12 m/s splits into two 0.5 kg halves; one moves off at 16 m/s at 90° to the original line. The speed of the other half is:
A. 20 m/s
B. 24 m/s
C. ≈ 28.8 m/s ✓ Correct
D. 16 m/s
Solution: Conserve both components. Perpendicular: 0.5×16 = 8 must be cancelled ⇒ other half v_y = −16 m/s. Along the line: 1×12 = 0.5v_x ⇒ v_x = 24 m/s. Speed = √(24² + 16²) = √832 ≈ 28.8 m/s.
Q8 — Conservation of Linear Momentum · medium · numerical
A 2 kg body at (4î) m/s and a 3 kg body at (−2î) m/s collide and stick. The final velocity is:
A. −0.4î m/s
B. 0.4î m/s ✓ Correct
C. 1î m/s
D. 2î m/s
Solution: v = (8 − 6)/5 = 0.4 m/s along +x.