Two bodies have their moments of inertia `I` and `2 I` respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio.

Options

A. `1:2`
B. `sqrt(2):1`
C. `1:sqrt(2)`
D. `2:1`

Answer

C

Explanation

`(L_(1)^(2))/(2I_(1))=(L_(2)^(2))/(2I_(1))implies (L_(1)^(2))/(2(I))=(L_(2)^(2))/(2(I))implies(L_(1))/(L_(2))=(1)/(sqrt2)`