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KVPY2017PhysicsRotational Motion

A solid cube of wood of side 2 a and mass M is resting on a horizontal surface as shown in the figure. The cube is free to rotate about the fixed axis AB . A bullet of mass m (

Options

  1. A3 gM / 2 ma
  2. B3 g / 4 h
  3. C3 g( 2 -1) / 2 a
  4. D3 g( 2 -1) / 4 a

Correct answer

D. 3 g( 2 -1) / 4 a

Step-by-step solution

conservation of energy array l 1 2 I _ A _ c ²= Mg ( a 2 - a ) I _ A = I _ cm + Ma ²= 2 3 Ma ²+ M ( a 2 )² I _ A = 8 9 Ma ² 1 2 8 3 Ma ² _ c ²= Mg a ( 2 -1) _ c = 3 ~g ( 2 -1) / 4 a array

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