Question

A hollow sphere of radius R lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. Find the distance travelled by the sphere during the time it makes one full rotation.

Answer 1

Taking moment about the centre of hollow sphere we will get,

$F\times R=\left(\frac{2}{3}\right)M{R}^2\alpha$

$\Rightarrow \alpha =\frac{3F}{2MR}$

$\text{Again,}2\pi =\frac{1}{2}a{t}^2$

$\text{(From}\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2)$

$\Rightarrow t^2=\frac{8\pi MR}{3F}$

$\Rightarrow a_c=\frac{F}{M}$

$\Rightarrow X=\frac{1}{2a_c}{t}^2$

=$\frac{1}{2}\times \frac{F}{M}\times \left(\frac{8\pi MR}{3F}\right)=\frac{4\pi R}{3}$