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

(d) As said, `(KE)_(rot)` remains same.
i.e., `(1)/(2) I_1 omega_1^2 = (1)/(2) I_2 omega_2^2`
`rArr (1)/(2 I_1)(I_1 omega_1)^2 = (I)/(2 I_2) (I_2 omega_2)^2`
`rArr (L_1^2)/(I_1) = (L_2^2)/(I_2)`
`rArr (L_1)/(L_2) = sqrt((I_1)/(I_2))`
but `I_1 = I, I_2 = 2 I`
:. `(L_1)/(L_2) = sqrt((I)/(2 I)) =(1)/(2)`
or `L_1 : L_2 = 1 : sqrt(2)`.