Thickness of a wooden circular plate is same as the thickness of a metal circular plate but density of metal plate is `8` times density of wooden plate. If moment of inertia of wooden plate is twice the moment of inertia of metal plate about their natural axes, then the ratio of radii of wooden plate to metal plate is

Options

A. `1:2`
B. `1:4`
C. `4:1`
D. `2:1`

Answer

D

Explanation

`I _(1) = 2I_(2) , M_(1)R_(1)^(2) = 2M_(2) R_(2)^(2)`
`((R_(1))/(R_(2)))^(2) = 2 (M_(2))/(M_(1)) , " but " m prop D xx R^(2) `
`(R_(1)/(R_(2))) ^(2) = 2 (D_(2))/(D_(1)) ((R_(2))/(R_(1)))^(2) = ((R_(1))/(R_(2)))^(4) = 2 (D_(2))/(D_(1))`