If I is the moment of inertial of a disc about an axis passing through its centre then find the change in moment of inertial due to small change in its moment of inertia due to small change in its temperature `Delta t`. `alpha` is the coefficient of linear expansion of disc.

Explanation

Moment of inertial of a disc of mass M, radius R about an axis passing through its centre and perpendicular to the plane of disc is
`I = 1/2 MR^(2)`
Then `Delta I = M/2 2 RDelta R = MRDeltaR`
`:. (Delta I)/(I) = (MRDelta R)/(MR^(2)//2) = (2DeltaR)/(R)`
But `(Delta R)/(R) = alpha Delta t`
therefore, `(Delta I)/(I) = 2 alpha Delta t or Delta I = 2 I alpha Deltat`.