Question

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is:_________.a) 2b) 8c) 4d) 10e) 6

Answer 1

The ratio of moment of inertia of larger sphere to that of smaller sphere = 4

Step-by-step explanation:

The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.

Radius of smaller sphere = D/2

Radius of larger sphere = 2D/2 = D.

Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10

Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5

The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4