It I is the moment of inertia of a distance about an axis passing through its centre the find the change in moment of inertia due to small change in its temperature `Delta t alpha` is the Coefficient of linear expeansion of distance .

Explanation

Moment of inertia of a distance of mass `M,` radius R about and axis passing through its centre & perpendicular to the plane of distance is
`I = (1)/(2) MR^(2)`
`Delta I = (M)/(2) . 2 R Delta R`
`(Delta I )/(I ) = (M)/((1)/(2)) = 2 (Delta R )/(R )`
`(Delta I )/(I ) = 2 alpha Delta t`
or `Delta I = 2I alpha Delta t`