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NEETPhysicsCenter of Mass, Momentum and Collision

A fixed smooth wedge has two faces, each inclined at an angle to the horizontal. Two identical blocks, each of mass m , are released simultaneously from rest at the top vertex and slide down the opposite faces. What should be the value of so that the magnitude of the total linear momentum of the two-block system at any time t is exactly equal to the momentum a single block of mass m would acquire if dropped freely fo

Options

  1. A30^
  2. B60^
  3. C90^
  4. D45^

Correct answer

D. 45^

Step-by-step solution

Let the speed of each block at time t be v . Since they slide down smooth inclines of angle , their acceleration is a = g . The speed at time t is v = (g )t . The velocity vectors of the two blocks are directed downwards along the inclines. Their horizontal components are equal and opposite, thus cancelling each other out. Their vertical components are both directed downwards with magnitude v . The magnitude of the total linear momentum of the system is P = 2m(v ) = 2m(g t) = 2mgt ^2 . The momentum of a single bloc

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