Two circular discs `A` and `B` of equal masses and thicknesses. But are made of metals with densities `d_A and d_B (d_A gt d_B)`. If their moments of inertia about an axis passing through the centre and normal to the circular faces be `I_A and I_B`, then.

Options

A. `I_A = I_B`
B. `I_A gt I_B`
C. `I_A lt I_B`
D. `I_A ge I_B`

Answer

C

Explanation

( c) mass = volume `xx` density `rArr M = (pi R^2 t)d`…(1)
where `t` is thickness
`I = (MR^2)/(2)` …(2)
From (1) and (2), we get :
`I = (M^2)/(2 pi dt) rArr I prop (1)/(d) rArr I_A lt I_B`.