Question

What is the moment of inertia for a solid sphere w.r.t. a tangent touching to its surface?

• A. $\frac{2}{5}MR^{2}$
• B. $\frac{7}{5}MR^{2}$
• C. $\frac{2}{3}MR^{2}$
• D. $\frac{5}{3}MR^{2}$

Answer 1

Answer: (B)

$\frac{7}{5}MR^{2}$

Answer 2

The moment of inertia for a solid sphere along its diameter is $I_{\text {diameter }}=\frac{2}{5} M R^{2}$ Moment of inertia about a tangent touching to its surface, $I_{\text {tangent }}=I_{\text {diameter }}+M R^{2}$ (using theorem of parallel axes) $=\frac{2}{5} M R^{2}+M R^{2}$ $=\frac{7}{5} M R^{2}$