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JEE MainPhysicsCenter of Mass, Momentum and Collision

A trolley of mass 400 kg is moving on a frictionless horizontal track with an initial velocity of 10 m/s. A sack of sand is dropped vertically into the trolley, causing the velocity of the trolley and sand combined to decrease to 8 m/s. The mass of the sack of sand is:

Options

  1. A500 kg
  2. B320 kg
  3. C800 kg
  4. D100 kg

Correct answer

D. 100 kg

Step-by-step solution

By the principle of conservation of linear momentum in the horizontal direction, the initial momentum of the trolley equals the final momentum of the trolley and the sand combined. Let the mass of the trolley be M = 400 kg and its initial velocity be v₁ = 10 m/s. Let the mass of the sand be m and the final velocity of the system be v₂ = 8 m/s. Since the sand is dropped vertically, it has no initial horizontal momentum. M v₁ = (M + m) v₂ 400 10 = (400 + m) 8 4000 = 3200 + 8m 8m = 800 m = 100 kg Answer: 100 kg

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