Question

A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is

• A. increases by 9%
• B. decreases by 9%
• C. increases by 6%
• D. decreases by 6%

Answer 1

Answer: (D)

In this case, angular momentum, $J=I \omega$
Taken, $v=1$
$v'=1.09$
and $\Delta v=0.09$
$\Rightarrow \omega \propto \frac{ 1 }{I}$
Bul $I \propto r^{2}$ and $\omega \propto v^{1 / 3}$
$\therefore \omega \propto \frac{1}{v^{2 / 3}}\left(\right.$ or $\left.v^{-2 / 3}\right)$
$\therefore $ Change in angular speed
$=\frac{\Delta \omega}{\omega} \times 100=-\frac{2}{3} \frac{\Delta v}{v} \times 100$
$=-\frac{2}{3} \times 0.03 \times 100=-6 \%$
So, angular speed will decrease with $6 \%$.