A uniform metallic disc of radius r and mass m is spinning with angular speed `omega_(0)` about an axis passing through its centre and perpendicular to plane. If its temperature is increased (slightly) by `DeltaT` its new angular speed is (The coefficient of linear expansion of the metal is `alpha`)

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)])`