A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the…
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
increases by 9%
decreases by 9%
increases by 6%
decreases by 6%
Solution
(d) In this case, angular momentum, $J=I \omega$
Taken,
$v=1$
$V^{\prime}=1.09$
and
$\Delta v=0.09$
$\Rightarrow$
$\omega \propto \frac{1}{I}$
But
$I \propto r^2 \text { and } \omega \propto v^{1 / 3}$
$\therefore$
$\omega \propto \frac{1}{v^{2 / 3}}\left(\text { or } v^{-2 / 3}\right)$
$\therefore$ Change in angular speed
$\begin{aligned}
& =\frac{\Delta \omega}{\omega} \times 100=-\frac{2}{3} \frac{\Delta v}{v} \times 100 \\
& =-\frac{2}{3} \times 0.03 \times 100=-6 \%
\end{aligned}$
So, angular speed will decrease with $6 \%$.