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. `n ^(2) omega`
D. `n omega`

Explanation

According to aw of conservation of angular momentum is no external torque is acting upon a body about an axis, then the angular momentum of the body
`L = I omega =`constant
`implies I _(1) omega _(1) = I _(2) omega _(2)`
Also `1= (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)`
`implies omega_(2) = n^(2) omega _(1) = n ^(2) omega `