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

D

Explanation

First Method :
Given : `(1)/(2)I_(1)omega_(1)^(2)=(1)/(2)(2I)omega_(2)^(2)`
`therefore" "(omega_(1))/(omega_(2))=sqrt2`
`therefore" "(L_(1))/(L_(2))=(I_(1)omega_(1))/(I_(2)omega_(2))=(1)/(2)xxsqrt2=(1)/(sqrt2)`
Second Method :
The relation between L and K is `L=sqrt(2KI)`
`therefore" "(L_(1))/(L_(2))=sqrt((2KI)/(2I(2I)))=(1)/(sqrt2)" "(because " same K for both")`