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. `2:1`
B. `1:2`
C. `sqrt2:1`
D. `1:sqrt2`

Answer

B

Explanation

First Method`" Given,"(1)/(2)l_(1)omega_(1)^(2)=(1)/(2)(2l)omega_(2)^(2)`
`therefore" "(omega_(1))/(omega_(2))=sqrt2`
`therefore" "(L_(1))/(L_(2))=(l_(1)omega_(1))/(l_(2)omega_(2))=(1)/(2)xx sqrt2 =(1)/(sqrt2)`
Second Method
The relation between L and K is `L=sqrt(2Kl)`
`therefore" "(L_(1))/(L_(2))=sqrt((2Kl)/(2K(2l)))=(1)/(sqrt2)" "(because "same K for both")`