Q 11-06-122JEE MainJEE Main 2023 (6 Apr, Shift 1)Medium
Two identical solid spheres each of mass $2\ \text{kg}$ and radii $10\ \text{cm}$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40\ \text{cm}$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is ______ $\times10^{-3}\ \text{kg m}^2$.
Numerical value type. Enter your answer.
Answer: 176
Each centre is $0.2\ \text{m}$ from the axis:
$$I=2\left(\frac25\times2\times0.01+2\times0.04\right)=2(0.008+0.08)=0.176\ \text{kg m}^2=176\times10^{-3}\ \text{kg m}^2$$
Solution by Sreeraj P, M.Sc Physics