Question 438: Centre of Mass and Rotational Motion

Question

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $$\sqrt x$$ cm. The value of $$x$$ is ________.

Accepted Answer

$$
\begin{aligned}
& \mathrm{I}_{\mathrm{cm}}=\frac{2}{5} \mathrm{MR}^2 \\
& \mathrm{I}_{\mathrm{PQ}}=\mathrm{I}_{\mathrm{cm}}+\mathrm{md}^2 \\
& \mathrm{I}_{\mathrm{PQ}}=\frac{2}{5} \mathrm{mR}^2+\mathrm{m}(10 \mathrm{~cm})^2
\end{aligned}
$$
For radius of gyration $\mathrm{I}_{\mathrm{PQ}}=\mathrm{mk}^2$
$$
\begin{aligned}
& \mathrm{k}^2=\frac{2}{5} \mathrm{R}^2+(10 \mathrm{~cm})^2 \\
& =\frac{2}{5}(5)^2+100 \\
& =10+100=110 \\
& \mathrm{k}=\sqrt{110} \mathrm{~cm} \\
& \mathrm{x}=110
\end{aligned}
$$

Centre of Mass and Rotational Motion

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $\sqrt x cm. The value of x$ is ________.

Integer / Numeric Answer Type