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. `2:1`
D. `1:sqrt(2)`

Answer

D

Explanation

`KE=(1)/(2)I omega^(2), KE=(L^(2))/(2I)`
`(KE_(1))/(KE_(2))=(L_(1)^(2))/(2I)xx(2xx2I)/(L_(2)^(2))`
implies `(1)/(2)=((L_(1))/(L_(2)))^(2)impliesL_(1):L_(2)=1:sqrt(2)`