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A solid sphere A of radius R and mass M is attached at a point to a smaller solid sphere B of radius r<R and mass m<M. Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of A is I_A and that calculated about a vertical axis passing through the centre of B is I_B. The difference I_A-I_B is :

Asked in Re-NEET 2026 · Composite and cavity bodies

• (1) (M-m)(R+r)²
• (2) (m-M)(R+r)²
• (3) (m-M)(R-r)²
• (4) 0

Step-by-step solution

Why the other options are wrong

• (1) The sign is reversed: this is I_B-I_A.
• (3) Uses R-r for the distance between the centres; spheres touching at one point have their centres R+r apart.
• (4) The terms about each sphere's own centre do cancel, but the parallel-axis terms m(R+r)² and M(R+r)² do not, since m eq M.

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