Question

If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a line parallel to itself will increase by
(a) zero
(b) αI∆t
(c) 2αI∆t
(d) 3αI∆t.

Answer 1

(c) 2αI∆t

The moment of inertia of a solid body of any shape changes with temperature as
$I\text{'}=I\left(1+2\alpha \Delta t\right)$
Here, I = initial moment of inertia
I' = new moment of inertia due to change in temperature
$\alpha$ = expansion coefficient
$\Delta$t = change in temperature
So, $I\text{'}-I=2\alpha I\Delta t$I−I0=2αΔt