A uniform brass disc of radius a and mass m is set into spinning with angular speed `omega_0` about an axis passing through centre of disc and perpendicular to the palne of disc. If its temperature increases from `theta_1^@C` to `theta_2^@C` with out disturbing the disc, what will be its new angular speed ?

Options

A. `omega_0[1+2a(theta_2-theta_1)]`
B. `omega_0[1+a(theta_2-theta_1)]`
C. `(omega_0)/([1+2alpha(theta_2-theta_2)])`
D. none of these

Answer

C

Explanation

From the conservation priciple of angular momentum
`L_i=L_f`
`I_0omega_0=Iomega`
Here, `I=I_0[1+2alpha(theta_2-theta_1)]`
`omega=(I_0omega_0)/(I_0[1+2alpha(theta_2-theta_1)])=(omega_0)/([1+2alpha(theta_2-theta_1)])`