Question

What is the moment of intertia 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)

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

Moment of inertia for a solid sphere with respect to a line passing through the center of sphere $=\frac{2}{5}M{R}^2$

From parallel axis theorem,

Moment of inertia of solid sphere with respect to tangent touching to its surface$=I^{\prime }=I_{CM}+M{r}^2=\frac{2}{5}M{R}^2+M(R{)}^2=\frac{7}{5}M{R}^2$