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

Options

A. `(omega)/(n)`
B. `(omega)/(n^(2))`
C. `nomega`
D. `n^(2)omega`

Answer

D

Explanation

By law of conservation of angular momentum, if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant that is, `J=l omega`
Also, `l=(2)/(5)MR^(2)` for a solid sphere,
Given, `R_(1)=R, R_(2)=(R)/(n)`
`therefore (2)/(5)MR^(2)omega_(1)=(2)/(5)M((R)/(n))^(2)xx omega_(2)" "rArr" "omega_(2)=n^(2)omega_(1)=n^(2)omega`