Question

The moment of inertia of a body is $I$ and its coefficient of linear expansion is $\alpha $ if the temperature of the body rises by a small amount $\Delta T$ . Then change in the moment of inertia about the same axis is

• A. $\alpha I\Delta T$
• B. $2\alpha I\Delta T$
• C. $4\alpha I\Delta T$
• D. $\frac{\alpha I \Delta T}{2}$

Answer 1

Answer: (B)

The expression of the moment of inertia of a body is
$I \propto m r^{2}\Rightarrow I=k m r^{2}$
and thermal expansion in dimension, $\Delta r=r\alpha \Delta T$
Now, fractional change in moment of inertia due to thermal expansion, $\frac{\Delta \, I}{I}=\frac{2 \Delta r}{r}=2 \, \alpha \, \Delta T$
or $\Delta I \, =2\alpha I \, \Delta T$