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

Answer

B

Explanation

`I prop omega_(1) = "----"(1) , I = (ML^(2))/3 rArr I prop L^(2) "---- " (2) `
from (1) and (2) `omega prop 1/(L^(2))`