Question

A rigid spherical body is spinning around an axis without any external torque. Due to temperature its volume increases by 3%. Then percentage change in its angular speed is

• A. $-2\%$
• B. $-1\%$
• C. $-3\%$
• D. $1\%$

Answer 1

The correct option is A $-2\%$

The moment of inertia of a solid sphere, $I=\frac{2}{5}m{R}^2$
or $I\propto R^2$

We know that volume $=\frac{4}{3}\pi R^3$
i.e., $V\propto R^3$
or $\frac{\Delta V}{V}\times 100=3\frac{\Delta R}{R}\times 100$
Percentage increase in volume is $3\%$
$\therefore$ Percentage increase in radius will be $1\%$.

$\therefore$ Percentage increase in moment of inertia will be $2\%$. As, $I\propto R^2$

Now, since angular momentum $L=I\omega$ will remain conserved. Hence, the angular velocity $\omega$ will decrease by $2\%$ to keep the angular momentum constant.

Hence option A is the correct answer.