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JEE MainPhysicsCenter of Mass, Momentum and Collision

Two blocks of masses 3 kg and 1 kg are tied to the ends of a light inextensible string which passes over a light frictionless pulley. The pulley is suspended from the ceiling of an elevator. The elevator is accelerating upwards with an acceleration of 2 m/s ^2 . The system is released from rest relative to the elevator. The distance traversed by the centre of mass of the two-block system with respect to the ground fr

Options

  1. A1
  2. B6
  3. C9
  4. D2

Correct answer

D. 2

Step-by-step solution

Let the masses be m₁ = 3 kg and m₂ = 1 kg. The upward acceleration of the elevator is a₀ = 2 m/s ^2 . The effective acceleration due to gravity in the elevator frame is: g_ eff = g + a₀ = 10 + 2 = 12 m/s ^2 The relative acceleration of the blocks with respect to the elevator is: a_ rel = m₁ - m₂ m₁ + m₂ g_ eff = 3 - 1 3 + 1 12 = 6 m/s ^2 Taking the upward direction as positive, the absolute acceleration of the heavier block ( m₁ ) in the ground frame is: a₁ = a₀ - a_ rel = 2 - 6 = -4 m/s ^2 The absolute acceleratio

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