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 .

Step-by-step solution

The moment of inertia of a sphere is given by the formula I = 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 × 2 5 M R 2 + M l 2 + r 2       . . . ( i ) The given data is M = 2   kg l = 0 . 4 - 0 . 2   m = 0 . 2   m R = 0 . 1   m Substituting the values in equation (i) I = 4 5 ( 2 × 0 . 1 2 ) + 2 × 2 ( 0 . 2 2 + 0 . 1 ) 2     kg   m 2 ⇒ I = 4 5 &#215