Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as 2 . The value of is _______.

Step-by-step solution

Moment of inertia of the rod about axis AB passing through one of its ends: I_ rod = ML^2 3 = 40 (3)^2 3 = 40 9 3 = 120 kg m ^2 Moment of inertia of the solid sphere about the same axis AB , using the parallel axis theorem I = I_ cm + md^2 : Mass m = 10 kg , radius R , distance from the centre of the sphere to axis AB is d = 3 m . I_ sphere = 2 5 mR^2 + md^2 = 2 5 (10)R^2 + 10(3)^2 = 4R^2 + 90 Equating the two moments of inertia: 120 = 4R^2 + 90 4R^2 = 30 R^2 = 15 2 R = 15 2 Comparing with R = 2 : = 15 Hence, = 15