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The angular velocity of a body is increa...

The angular velocity of a body is increased from 5 rad/s to 20 rad/s, without applying a torque but by changing its moment of Inertia. What is the relation between the new radius of gyration and the initial radius of gyration?

A

`K_(1)=K_(2)`

B

`K_(1)=(K_(2))/(2)`

C

`K_(1)=2K_(2)`

D

`K_(2)=3K_(1)`

Text Solution

Verified by Experts

The correct Answer is:
C
As per the principle of conservation of angular momentum,
`I_(1)omega_(1)=I_(2)omega_(2)`
But `I=MK^(2)`
`therefore MK_(1)^(2)omega_(1)=MK_(2)^(2)omega_(2)" [K is the radius of gyration]"`
`therefore (K_(1))/(K_(2))=sqrt((omega_(2))/(omega_(1)))=sqrt((20)/(5))=2`
`therefore K_(1)=2K_(2)`
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