Question

Moment of inertia of solid sphere about its diameter I. If that sphere is recast into 8 identical small spheres, then the moment of inertia of a small about its diameter is

• A. $\frac{I}{8}$
• B. $\frac{I}{16}$
• C. $\frac{I}{24}$
• D. $\frac{I}{32}$

Answer 1

The correct option is D $\frac{I}{32}$

$\begin{array}{c}\text{We know that moment of Inertia of a sphere}\\ \text{about its diameter is = I}\\ \text{Let the mass of sphere be(M), of Radius (R)}\\ \Rightarrow I=\frac{2}{5}M{R}^2\end{array}$

$\begin{array}{c}\text{For small eight equal spheres -}\\ \text{mass}m=\frac{M}{8}\text{radius}r=\frac{R}{2}\\ \Rightarrow \text{I of sunaller spheres will be-}\\ \begin{array}{c}{I}_{\text{sm}}=\frac{2}{5}\times \frac{M}{8}\times {\left(\frac{R}{2}\right)}^2=\frac{1}{32}\times \frac{2}{5}M{R}^2\\ \text{Hence, option (D) is correct.}\end{array}\end{array}$