Question 482: Centre of Mass and Rotational Motion

Question

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is

Accepted Answer

$$ \mathrm{I}=\frac{2}{5} \mathrm{MR}^2 $$
For smaller spheres mass $\mathrm{M}^{\prime}=\frac{\mathrm{M}}{27}$
Radius of each smaller sphere $=\mathrm{R}^{\prime}=\frac{\mathrm{R}}{3}$
$$ \begin{aligned} 	herefore \quad I^{\prime} & =\frac{2}{5} M^{\prime} R^{\prime 2}=\frac{2}{5} 	imes \frac{M}{27} 	imes \frac{R^2}{9} \ & =\frac{1}{243}\left(\frac{2}{5} M^2ight)=\frac{1}{243} \end{aligned} $$

Answer

$\frac{1}{44}$

Answer

$\frac{\mathrm{I}}{188}$

Answer

$\frac{1}{204}$

Answer

$\frac{1}{243}$

Centre of Mass and Rotational Motion

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is

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