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Two bodies have their moments of inertia...

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.

A

`1:2`

B

`sqrt2:1`

C

`2:1`

D

`1: sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
D
`KE= (1)/(2) I omega^(2) , KE= (L^(2))/(2I)`
`(KE_(1))/(KE_(2))= (L_(1)^(2))/(2I) xx (L^(2))/(2I)`
`(KE_(1))/(KE_(2))= (L_(1)^(2))/(2I) xx (2 xx 2I)/(L_(2)^(2))`
`rArr (1)/(2) = ((L_(1))/(L_(2)))^(2) rArr L_(1) : L_(2)= 1 : sqrt2`
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