A massless string is wrapped around a hollow cylinder having mass `m` and radius `r`. The cylinder is kept on a rough horizontal surface (coefficient of friction is `mu`). A constant force `F` is applied as shown in the figure. In case of pure rolling, the friction force acting on the bottom most point of the cylinder is

Options

A. zero
B. `mu mg`
C. `mu mg//2`
D. `3mu mg//2`

Explanation

`F+f_(r)=ma_(c )`….(`1`)
Anticlockwise is taken as positive.
`R(F-f_(t))=I(a_(c ))/(R )`, where `I=mR^(2)`….(`2`)
So, `f_(r)=0`