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Solve the following :

Question:

A hollow sphere of radius $R$ lies on 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.

Solution:

$\tau=I \alpha$

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

$\alpha=\frac{3 F}{2 M R}$

Time to complete one rotation

$\quad \theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$

By, $2 \pi=\frac{1}{2}\left(\frac{3 F}{2 M R}\right) t^{2}$

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