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KCET2016PhysicsRotational Motion

Three bodies a ring ( (R) ), a solid cylinder ( (C) ) and a solid sphere ( (S) ) having same mass and same radius roll down the inclined plane without slipping. They start from rest, if ( v_ R , v_ c ) and ( v_ s ) are velocities of respective bodies on reaching the bottom of the plane, then

Options

  1. A( v_ R =v_ C =v_ S )
  2. B( v_ R >v_ C >v_ S )
  3. C( v_ R < v_ C < v_ S )
  4. D( v_ R =v_ C >v_ S )

Correct answer

C. ( v_ R < v_ C < v_ S )

Step-by-step solution

The velocity of a body rolling without slipping down oninclined plane is given as [ v= 2 g h 1+K² / R² ] Here, ( K ) is the radius of gyration. For ring, ( K=R ) [ v_ R = g h ] For solid sphere, ( K= 2 5 R ) [ v_ s = 10 g h 7 ] For solid cylinder, ( K= R 2 ) [ v_ c = 4 g h 3 ]

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