A circular disc P of radius R is made from an iron plate of thickness t and another disc Q of radius
2R is made from an iron plate of thickness `(t)/(2)`.
The relation between their moments of inertia `I_(p)` and `I_(Q)` about their natural axes is

Options

A. `I_(Q)=4I_(P)`
B. `I_(P)=8I_(Q)`
C. `I_(P)=4I_(Q)`
D. `I_(Q)=8I_(P)`

Answer

D

Explanation

`I_(P)=(MR^(2))/(2)`
`(((pi R^(2))t)rho(R^(2)))/(2)=(pi t rho R^(4))/(2)`
`I_(Q)=(MR^(2))/(2)`
`=((pi(2R)^(2)(t//2))rho(2R)^(2))/(2)`
`= (pi t rho(8 R^(4)))/(2)=8I_(P)`.