Question

A lawn roller in the form of a thin-walled hollow cylinder of mass $M$ is pulled horizontally with a constant horizontal force $F$ applied by a handle attached to the axle. Ifit rolls without slipping, find the acceleration and the friction force.

Answer 1

$I=M{R}^2$ For pure rolling to take place. $a=R\alpha$
or $\frac{F-f}{M}=R\left(\frac{f.R}{M{R}^2}\right)=\frac{f}{M}$
$\therefore f=\frac{F}{2}$ and
$a=\frac{F-f}{M}=\frac{F}{2M}$