Question

The moment of inertia of a thin spherical shell of mass M and radius R about a diameter is $\frac{2}{3}$ MR 2Its radius of gyration K about a tangent will be

• A. $\sqrt{\frac{2}{3}}R$
• B. $\frac{2}{3}R$
• C. $\frac{5}{3}R$
• D. $\sqrt{\frac{5}{3}}R$

Answer 1

Answer: (D)

$\sqrt{\frac{5}{3}}R$

Answer 2

Moment of inertia of shell about a tangent $I={{I}_{G}}+M{{R}^{2}}$ $I=\frac{2}{3}M{{R}^{2}}+M{{R}^{2}}=\frac{5}{3}M{{R}^{2}}$ $\therefore$ $M{{K}^{2}}=\frac{5}{3}M{{R}^{2}}$ $K=\sqrt{\frac{5}{3}}R$