From a solid sphere of mass M and radius 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

Engineering

Physics

Moment of Inertia

Question

$\frac{{MR}^{2}}{32 \sqrt{2} π}$

$\frac{{MR}^{2}}{16 \sqrt{2} π}$

$\frac{4 {MR}^{2}}{3 \sqrt{3} π}$

$\frac{4 {MR}^{2}}{9 \sqrt{3} π}$

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$2 R = \sqrt{3} ℓ$

$ℓ = \frac{2 R}{\sqrt{3}}$

$\frac{M}{\frac{4}{3} {πR}^{3}} = \frac{M_{1}}{ℓ^{3}} = \frac{M_{1}}{\frac{8}{3 \sqrt{3}} R^{3}}$

$M_{1} = \frac{2 M}{\sqrt{3} π}$

$I = \frac{1}{6} M_{1} (2 ℓ^{2}) = \frac{1}{3} \times \frac{2 M}{\sqrt{3} π} \times \frac{4 R^{2}}{3} = \frac{4 {MR}^{2}}{9 \sqrt{3} π}$