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

Answer 1

Answer: (C)

$\frac{137}{15}M{R}^2$

For Ball
using parallel axis theorem.

$I_{ball}=\frac{2}{5}M{R}^2+M(2R{)}^2$

$=\frac{22}{5}M{R}^2$

2 Balls so $\frac{44}{5}M{R}^2$

Irod = for rod $\frac{M(2R{)}^2}{R}=\frac{M{R}^2}{3}$

$I_{system}=I_{Ball}+I_{rod}$

$=\frac{44}{5}M{R}^2+\frac{M{R}^2}{3}$

$=\frac{137}{15}M{R}^2$