Question

A horizontal force is applied on spherical shell of radius $R$ placed on rough surface. For what height h of force applied on shell will the shell always perform pure rolling motion irrespective of magnitude of force applied?

• A. $\frac{5}{3}R$
• B. $\frac{3}{2}R$
• C. $\frac{7}{3}R$
• D. $\frac{7}{5}R$

Answer 1

The correct option is A $\frac{5}{3}R$

For pure rolling, friction will be absent. So force F provides the torque required for rolling.

F = $ma$ & Fy = $I\alpha =\frac{2}{3}m{R}^2\alpha$
also $a=R\alpha$ so $\Rightarrow$ Fy=$\frac{2}{3}m\text{/}{R}^2\frac{a}{\text{/}R}$
$may=\frac{2}{3}mRa\Rightarrow y=\frac{2}{3}R$ $\Rightarrow h=R+y=\frac{5}{3}R$