Question

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 :

• A. $\frac{152}{15} MR^{2}$
• B. $\frac{17}{15} MR^{2}$
• C. $\frac{137}{15} MR^{2}$
• D. $\frac{209}{15} MR^{2}$

Answer 1

Answer: (C)

$\frac{137}{15} MR^{2}$

Answer 2

For Ball using parallel axis theorem.
$I_{\text{ball}} = \frac{2}{5} MR^{2} +M\left(2R\right)^{2}$
$=\frac{22}{5} MR^{2}$
$2$ Balls so $\frac{44}{5}MR^{2}$
Irod = for rod $\frac{M\left(2R\right)^{2}}{R} =\frac{MR^{2}}{3}$
$I_{\text{system}} =I_{\text{Ball}} +I_{\text{rod}}$
$= \frac{44}{5} MR^{2} + \frac{MR^{2}}{3}$
$= \frac{137}{15} MR^{2}$