Question

A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed

• A. Will increase approximately by 1 %
• B. Will decrease approximately by 1 %
• C. Will decrease approximately by 0.67 %
• D. Will increase approximately by 0.33 %

Answer 1

Answer: (C)

Will decrease approximately by 0.67 %

Volume of spherical body, $V=\frac{4}{3}\pi R^3$
$\Rightarrow \frac{\Delta V}{V}=3\frac{\Delta R}{R}$
$\Rightarrow \frac{\Delta R}{R}=0.33$

As there is no external torque angular momentum is conserved,
$L=I\omega$
$\Rightarrow L=\frac{2}{5}M{R}^2\omega$

$\Rightarrow \frac{\Delta L}{L}=2\frac{\Delta R}{R}+\frac{\Delta \omega }{\omega }$

Since, $\frac{\Delta L}{L}=0$ as the magnitude is constant.

$\Rightarrow \frac{\Delta \omega }{\omega }=-2\frac{\Delta R}{R}$

Therefore, $\omega$ decreases by $0.67\%$.