A solid sphere of mass ma nd radis R is placed on a rough horizontal surface A horizontal force F is applied to sphere at a height h, `(0lehleR)` from centre. If sphere rolls slipping then,

Options

A. The maximum possible acceleration of sphere is `(F)/(M)`
B. The maximum possible acceleration of sphere is `(10F)/(7M)`
C. The magnitude of friction force acting on the sphere is zero if `h=(2R)/(5)`
D. The magnitude of friction force acting on the sphere is zero `h=(3R)/(4)`.

Answer

B, C

Explanation

`F-f=ma_(cm)` .(i)
`Fh+fR=(2)/(5)mR^(2)(a_(cm))/(R)` .(ii)
(i) & (ii) `a_(cm)=(5F)/(7M)[1+(h)/(R)]`
`(a_(cm))_(max)=(10F)/(7M)`
`f_(max)=(3F)/(7)`