The temperature of uniform rod of length L having a coefficient of linear expansion `alpha_(L)` is changed by `Delta T` . Calculate the new moment of inertia of the uniform rod about axis passing through its center and perpendicular to an axis of the rod.

Explanation

Moment of inertia of a uniform rod of mass and length l about its perpendicular bisector.
Moment of inertia of the rod
`I=(1)/(12)ML^(2)`

Increase in length of the rod when temperature is increased by `DeltaT`, is given by
`L.=L(1+alpha_(L)DeltaT)`
New moment of inertia of the rod
`I.=(ML.^(2))/(12)=(M)/(12)L^(2)(1+alpha_(L)DeltaT)^(2)`
`I.=I(1+alpha_(L)DeltaT)^(2)`