A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness `t//4`. The relation between the moments of inertia `I_(A)` and `I_(B)` is (about an axis passing through centre and perpendicular to the disc)

Options

A. `I_(Y) = 32 I_(X)`
B. `I_(Y) = 16 I_(X)`
C. `I_(Y)= I_(X)`
D. `I_(Y) = 64 I_(X)`

Answer

D

Explanation

Mask of disck X, `m_(x) = piR^(2)trho`, where `rho` is the density of the material of the disc.
`therefore I_(N) = 1/2m_(x)R^(2) =1/2piR^(2)trho R^(2) = 1/2pi rho tR^(4)`
Mass of disc, Y,
`m_(y) = pi(4r)^(2) t/4 rho =4pi R^(2) trho therefore I_(Y) = 1/2m_(y)(4R)^(2)=1/24piR^(2)trho xx 16 R^(2) = 32pi t rho R^(2) rArr I_(Y) = 64 I_(X)`