A circular disc A of radius r is made from aniron plate of thickness t and nother circular disc B of rdius 4r is made fro an iron plate of thickness t/4. The relatiion between the moments of inertia `I_A and I_B` is

Options

A. `I_A gt I_B`
B. `I_A = I_B`
C. `I_A lt I_B`
D. depends on the actual values of `t` and `r`.

Answer

C

Explanation

( c) `m_A = volume xx density = pi r^2 t rho`
`I_A = (1)/(2) m_A r^2 = (1)/(2) pi r^4 rho t`
Similarly `I_B = (1)/(2) pi (4 r)^4 rho((t)/(4)) = 64 I_A`
Clearly `I_B gt I_A`.