Question

A uniform rod of length $L$ pivoted at one end $P$ is freely rotated in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through $P$. If the temperature of the system is increased by $\Delta T$, angular velocity becomes $\frac{\omega}{2}$. If coefficient of linear expansion of the rod is $\alpha(\alpha < < 1)$, then $\Delta T$ will be

• A. $\frac{1}{\alpha}$
• B. $\frac{1}{2 \alpha}$
• C. $\frac{1}{4 \alpha}$
• D. $\alpha$

Answer 1

Answer: (B)

$I \omega=I_{1} \frac{\omega}{2}$
$I_{1}=2 I$
$\frac{m l_{1}^{2}}{3}=2 \frac{m l_{0}^{2}}{3}$
$\left\{l_{0}^{2}(1+\alpha \Delta T)\right\}^{2}=2 l_{0}^{2}$,
$\therefore 1+2 \alpha \Delta T=2$
$ \therefore \Delta T=\frac{1}{2 \alpha}$