Question

A solid sphere lying on a smooth horizontal surface is pulled by a force acting on its top most point. What will be the distance traveled by the sphere during the time it makes one complete revolution?

Answer 1

$s=ut+\frac{1}{2}a{t}^2$

$=0+\frac{1}{2}\times \frac{F}{m}\times \frac{4\pi }{\alpha }$

$=\frac{1}{2}\times \frac{F}{m}\times 4\pi \times \frac{1}{\frac{\tau }{I}}$

$=\frac{F}{m}\times 2\pi \times \frac{1}{\frac{R\times F}{\frac{2}{3}m{R}^2}}$

$=\frac{F}{m}\times 2\pi \times \frac{2mR}{3F}$

$=\frac{4\pi R}{3}$