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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

A space-ship travelling in the interstellar medium is picking up dust at a rate d M d t = α v , where α is a positive constant, v is the instantaneous velocity and M is the total mass of the space-ship at any instant. The instantaneous acceleration of the space-ship is

Options

  1. A− 2 α v 2 M
  2. B− α v 2 M
  3. C− α v 2 2 M
  4. D− α v 2

Correct answer

B. − α v 2 M

Step-by-step solution

d M d t = α v F thrust = - v d M d t = M a ⇒ - v α v = M a ⇒ a = − α v 2 M

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