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A solid sphere is rotating about a diame...

A solid sphere is rotating about a diameter at an angular velocity `omega`. If it cools so that its radius reduces to `1//n` of its original value, its angular velocity becomes

A

`n^(2)omega`

B

`nomega`

C

`(omega)/(n^(2))`

D

`(omega)/(n)`

Text Solution

Verified by Experts

The correct Answer is:
A
The M.I. of the solid sphere `=(2)/(5)MR^(2)`
As no external torque is acting on the sphere, its angular momentum is conserved.
`therefore L_(1)=L_(2)" "therefore I_(1)omega_(2)=I_(2)omega_(2)`
`therefore" "(2)/(5)MR^(2)omega_(1)=(2)/(5)M((R)/(n))^(2)omega_(2)" "(because R_(2)=(R)/(n))`
`therefore" "omega_(2)=n^(2)omega_(1) or n^(2)omega`
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