Two circular loops `A` and `B` are made of the same wire and their radii are in the ratio `1:n`. Their moments of inertia about the axis passing through the centre and perpendicular to their planes are in the ratio `1:m`. The relation between `m` and `n` is

Options

A. `m=n`
B. `m=n^(2)`
C. `m=n^(3)`
D. `m=n^(4)`

Answer

C

Explanation

`(I_(1))/(I_(2))=(M_(1)R_(1)^(2))/(M_(2)R_(2)^(2))` for a circular loop, `MalphaR`
`:. (I_(1))/(I_(2))=(R_(1)^(3))/(R_(2)^(3))`