Question

the moment of inertia of earth is is mass and radius of earth are doubled what will be the moment of inertia

Answer 1

The moment of inertia will eight times the initial value.

The Earth acts like a solid sphere , the moment of inertia of a solid sphere = 2/5 MR²

Initial moment of inertial of Earth = 2/5 MR²

M - mass of the earth

R - radius of the earth

When the radius and the mass of the earth are doubled , M' = 2M and R' = 2R

Final moment of inertia of the earth = 2/5 M'R'²

= 2/5 × 2M × 4R²

= 16/5 MR²

The final moment of inertia of Earth is eight times the initial moment of inertia.