Question 494: Centre of Mass and Rotational Motion

Question

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter?
[ $\mathrm{I}_{\mathrm{h}}=$ moment of inertia of hollow sphere about an axis coinciding with its diameter, $\mathrm{I}_5=$ moment of inertia of solid sphere about an axis coinciding with its diameter]

Accepted Answer

$$ \begin{array}{ll} 	herefore & \mathrm{I}_{\mathrm{s}}=\frac{2}{5} \mathrm{MR}^2, \mathrm{I}_{\mathrm{h}}=\frac{2}{3} \mathrm{MR}^2 \ 	herefore & \frac{\mathrm{I}_{\mathrm{s}}}{\mathrm{I}_{\mathrm{h}}}=\frac{\left(\frac{2}{5} \mathrm{MR}^2ight)}{\left(\frac{2}{3} \mathrm{MR}^2ight)}=\frac{3}{5}\mathrm{I}_{\mathrm{s}} \end{array} $$

Answer

$\mathrm{I}_{\mathrm{s}}>\mathrm{I}_{\mathrm{h}}$

Answer

$\quad I_h \geqslant I_s$

Answer

$\mathrm{I}_{\mathrm{h}}>\mathrm{I}_{\mathrm{s}}$

Answer

$I_h=I_s$

Centre of Mass and Rotational Motion

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