Question 421: Centre of Mass and Rotational Motion

Question

A solid sphere of mass $$500 \mathrm{~g}$$ and radius $$5 \mathrm{~cm}$$ is rotated about one of its diameter with angular speed of $$10 ~\mathrm{rad} ~\mathrm{s}^{-1}$$. If the moment of inertia of the sphere about its tangent is $$x 	imes 10^{-2}$$ times its angular momentum about the diameter. Then the value of $$x$$ will be ___________.

Accepted Answer

$$
\begin{aligned}
& L_{	ext {diameter }}=\frac{2}{5} M R^2 \omega ; \quad I_{	ext {tangent }}=\frac{7}{5} M R^2 \\
& \begin{aligned}
\frac{I_{	ext {tangent }}}{L_{	ext {diameter }}} & =\frac{7 / 5}{2 / 5} 	imes \frac{1}{\omega}=\frac{7}{2 \omega} \\
& =\frac{7}{2 	imes 10}=\frac{7}{20} \\
&= \frac{700}{20} 	imes 10^{-2}=35 	imes 10^{-2}
\end{aligned}
\end{aligned}
$$

Centre of Mass and Rotational Motion

Choose the correct answer: