In the figure mass of both spherical body and block is m. Moment of inertia of the spherical body about center of mass is 2mR². The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is

 

detailed solution

Correct option is C

Let v be the linear velocity of center of mass of the spherical body and ω its angular velocity about centre of mass. ThenAs there is no slipping at B,  v=ω2R ⇒ω=v2RK.E. of spherical body,K1=12mv2+12Iω2=12mv2+12(12m(2R)2)v24R2=34mv2   ...............(i)Let say speed of the block is v'. There is no slipping at A ,  v+Rω=v' ⇒R2ω+Rω=v'⇒v'=(ω)(3R)=3Rω=(3R)v2R=32v∴ K.E. of block K2=12mv′2=12m32v2=98mv2…........ (ii)  From equations (i) and (ii), K1K2=23