Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

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Answer & Solution

Correct Answer

(A) \(\frac{{137}}{{15}}M{R^2}\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{l}
l = 2\left[ {\frac{2}{5}M{R^2} + M4{R^2}} \right] + M\frac{{4{R^2}}}{{12}}\\
\,\,\, = M{R^2}\left[ {\frac{1}{3} + \frac{4}{5} + 8} \right] = \frac{{137}}{{15}}M{R^2}
\end{array}\)

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