If the temperature of a uniform rod is slightly increased by Δt, its moment of inertia I about a perpendicular bisector increase by

Moment of inertia of a uniform rod is

when the temperature is increased by ∆t then increased length is

the moment of inertia is

there is only a slight change in length so a² (∆T)² value is very less, so we can ignore this term.

Hence, the increase in moment of inertia is

Hence, option C is the correct option.