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`
C. `1 : sqrt 2`
D. `2/1`

Answer

C

Explanation

As `K_(R_(1))= K_(R_(2))`
`therefore 1/2I_(1)omega_(1)^(2)=1/2I_(2)omega_(2)^(2)`
or `omega_(1)/omega_(2) = sqrt(I_(2)/I_(1))` ………………..(i)
`L_(1)/L_(2) = (I_(1)omega_(1))/(I_(2)omega_(2)) = (I_(1)/I_(2))sqrt(I_(2)/I_(1) = sqrt(I_(1)/I_(2)` (Using i)
`L_(1)/L_(2) = sqrt(1/2) = 1/sqrt(2)`