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The moment of inertia of a collapsing st...

The moment of inertia of a collapsing star changes to one-third of its initial value. The ratio of the new rotational kinetic energy to the initial rotational kinetic energy is ___

A

`3:1`

B

`1:3`

C

`9:1`

D

`1:9`

Text Solution

Verified by Experts

The correct Answer is:
A
Rotational K.E., `E= (1)/(2) 1omega^(2) " ""or", 2 E1 = (1 omega)^(2)`
Angular momentum `1omega = sqrt(2EI)`
In absence of any external torque the net angular momentum of the system remains conserved. Thus ,
`sqrt(2E_(1)I_(1))= sqrt(2E_(2)I_(2))` ltbegt `(E_(2))/(E_(1))=(I_(1))/(I_(2))=(3)/(1)`
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