Question

A ring of mass m and radius R is acted upon by a force F as shown in the figure, there is sufficient friction between the ring and the group then the force of friction force necessary for pure rolling is

Answer 1

REF.Image

The FBD will be as

$a=\alpha R$ [Pure rolling ] ___ (i)

$F-fk=ma$ ___ (ii)

As, $T=I\alpha$

$\Rightarrow (F+fk)R=M{R}^2\alpha$ ___ (iii)

From (i), (ii) and (iii), we get

$F-fk=F+fK\Rightarrow 2fk=0$

$\Rightarrow fk=0N$

No friction is required for pare rolling