Question

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is __________ × 10^{-3} kg-m^2

Answer 1

Using parallel axix theorem,
$\begin{aligned} & I_{s y s}=\left(\frac{2}{5} m r^2+m d^2\right) \times 2 \\\ & \Rightarrow I_{s y s}=\left(\frac{2}{5} \times 2 \times 0.01+2 \times 0.04\right) \times 2=(0.008+0.08) \times 2=0.088 \times 2=176 \times 10^{-3} \end{aligned}$