A uniform metal rod of length L and mass M is rotating about an axis passing through one of the ends and perpendicular to the rod with angular speed omega. If th temperature increases by `t^(@)C`, then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod = a)

Options

A. `sqrtomega`
B. `omega`
C. `omega^(2)`
D. `(1)/(omega)`

Answer

(b)

Explanation

According to conservation of angular momentum
`L=I_(1)omega_(1)=I_(2)omega_(2)=`Constant
Change of angular velocity, `Deltaomega=omega_(2)-omega_(1)`
`=(L)/(I_(2))-(L)/(I_(1))`
implies`Deltaomega=L=[(I)/(I_(2))-(I)/(I_(1))]`
implies`Deltaomega=L=[(I_(1)-I_(2))/(I_(1)I_(2))]`
implies `Deltaomega=(L)/(I_(1))[(I_(1))/(I_(2))-1]`
=`omega_(1)[(I_(1))/(I_(2))-1]`
because `Deltaomegaaomega`