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_(A)=I_(B)`
B. `I_(A)gt I_(B)`
C. `I_(B)gt I_(A)`
D. data is insufficient

Answer

C

Explanation

`(I_(A))/(I_(B))=(M_(A)R_(A)^(2))/(M_(B)R_(B)^(2))=(rho A_(A)xx t_(A)R_(A)^(2))/(rho A_(B)xx t_(B)R_(B)^(2))`
`= (pi R_(A)^(2)xx t_(A)xx R_(A)^(2))/(pi R_(B)^(2)xx t_(B)xx R_(B)^(2))`
`= (t_(A))/(t_(B))xx((R_(A))/(R_(B)))^(4)`
`= ((x)/(4))xx ((R )/(4R))^(4)`
`= 4xx (1)/(4^(4)`
`=(I_(A))/(I_(B))=(1)/(4^(3))`
`= (1)/(64)`
`I_(B)gt I_(A)`.