NEET Physics Question (2026) — Solution

Step-by-step solution

The distance between the centres of the two spheres A and B is d = R + r. Let I_ A, cm and I_ B, cm be the moments of inertia of spheres A and B about their respective vertical centroidal axes. For solid spheres, I_ A, cm = 2 5 MR^2 and I_ B, cm = 2 5 mr^2. The moment of inertia of the system about a vertical axis passing through the centre of A is given by the sum of the moment of inertia of A about its own centre and the moment of inertia of B about the centre of A. Using the parallel axis theorem: I_A = I_ A, cm + [ I_ B, cm + m(R+r)^2 ] Similarly, the moment of inertia of the system about a vertical axis passing through the centre of B is: I_B = [ I_ A, cm + M(R+r)^2 ] + I_ B, cm Now, finding the difference I_A - I_B: I_A - I_B = ( I_ A, cm + I_ B, cm + m(R+r)^2 ) - ( I_ A, cm + M(R+r)^2 + I_ B, cm ) I_A - I_B = m(R+r)^2 - M(R+r)^2 I_A - I_B = (m - M)(R+r)^2 Answer: (m-M)(R+r)^2