CBSE Class 12-science Answered

As shown in figure , if the dumble make a movement of one vertical revolution about the hinge point O ,

then the vertical displacement made by center of mass C of dumbell is 3l , where l is distance between spheres of dumbell.

If the sphere A moves with velocity u , then center of mass C will move with velocity  [ u / (2l) ] × [ (3l)/2 ] = (3/4)u

Hence , to make one complete circle , kinetic energy of center of mass at bottom should be equal to potential energy of center of mass at top.