From a solid sphere of mass
Question:

From a solid sphere of mass $\mathrm{M}$ and radius $\mathrm{R}$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is:-

1. $\frac{4 \mathrm{MR}^{2}}{9 \sqrt{3} \pi}$

2. $\frac{4 \mathrm{MR}^{2}}{3 \sqrt{3} \pi}$

3. $\frac{\mathrm{MR}^{2}}{32 \sqrt{2} \pi}$

4. $\frac{\mathrm{MR}^{2}}{16 \sqrt{2} \pi}$

Correct Option: 1

Solution: