Two identical solid spheres each of mass 2kg and radii 10cm are...

The moment of inertia of a sphere is given by the formula $I = \dfrac{2}{5}M{R}^{2}$.

Since there are two masses, the total moment of inertia about the axis perpendicular to the rod passing through the centre is

$I = 2 \times \left[\dfrac{2}{5}M{R}^{2} + M{\left(\dfrac{l}{2} + r\right)}^{2}\right] . . . ( i )$

The given data is

$M = 2kgl = \left(0 . 4 - 0 . 2\right)m = 0 . 2mR = 0 . 1m$

Substituting the values in equation (i)

$I = \left(\dfrac{4}{5} ( 2 \times 0 . {1}^{2} ) + 2 \times 2 ( \dfrac{0 . 2}{2} + 0 . 1{)}^{2}\right)kg{m}^{2} ⇒ I = \left(\left(\dfrac{4}{5} \times 0 . 02\right) + \left(4 \times 0 . 04\right)\right)kg{m}^{2} ⇒ I = \left(0 . 016 + 0 . 16\right)kg{m}^{2} = 0 . 176kg{m}^{2}$