Question 501: Centre of Mass and Rotational Motion

Question

Three spheres, each of mass ' $m$ ' and radius ' $r$ ' are placed as shown in figure. Consider an axis $\mathrm{YY}^{\prime}$, which is touching two spheres and passing through the diameter of third sphere. The moment of inertia of the system consisting of these three spheres about $\mathrm{YY}^{\prime}$ axis is

Accepted Answer

Moment of inertia of a solid sphere $=\frac{2}{5} \mathrm{mr}^2$
Moment of inertia of the upper sphere $=\frac{2}{5} \mathrm{mr}^2$
For each lower sphere M.I. $=\frac{2}{5} \mathrm{mr}^2+\mathrm{mr}^2$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, =\frac{7}{5} \mathrm{mr}^2 $$
Total moment of inertia $\mathrm{I}=\frac{2}{5} \mathrm{mr}^2+2 	imes \frac{7}{5} \mathrm{mr}^2$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, =\frac{16}{5} \mathrm{mr}^2 $$

Answer

$\frac{7}{5} \mathrm{mr}^2$

Answer

$\frac{2}{5} \mathrm{mr}^2$

Answer

$\frac{16}{5} \mathrm{mr}^2$

Answer

$\frac{\mathrm{mr}^2}{2}$

Centre of Mass and Rotational Motion

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