Four identical uniform solid spheres each of same mass ' M ' and radius ' R ' are placed touching each other as shown in figure, with centres A, B, C, D . I_A, I_B, I_C and I_D are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in I _ A , and I _ B is

Step-by-step solution

Using the parallel axes theorem, the M.I. of the system about the axis passing through the centre of the sphere A is aligned I _ A = I _ A ^ + I _ B ^ + I _ C ^ + I _ D ^ & I _ A = 2 5 MR ^2+ ( 2 5 MR ^2+4 MR ^2 ) & + ( 2 5 MR ^2+16 MR ^2 ) & + ( 2 5 MR ^2+36 MR ^2 ) aligned I _ A =57.6 MR ^2 The M.I. about sphere B is, aligned I _ B = 2 5 MR ^2+ ( 2 5 MR ^2+4 MR ^2 ) & + ( 2 5 MR ^2+16 MR ^2 ) & + ( 2 5 MR ^2+4 MR ^2 ) I _ B =25.6 MR ^2 & I _ A - I _ B =57.6 MR ^2-25.6 MR ^2=32 MR ^2 aligned