Q147 / 155 · WBJEE 2021 · Physics

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 $\mathrm{P}$. If the temperature of the system is increased by $\Delta \mathrm{T}$, angular velocity becomes $\frac{\omega}{2}$. If coefficient of linear expansion of the rod is $\alpha(\alpha< < 1)$, then $\Delta \mathrm{T}$ will be

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

Solution

$\mathrm{I} \omega=\mathrm{I}_{1} \frac{\omega}{2}$ $\quad \mathrm{I}_{1}=2 \mathrm{I}$ $\quad \frac{\mathrm{ml}_{1}^{2}}{3}=2 \frac{\mathrm{ml}_{0}^{2}}{3}$ $\left\{\mathrm{I}_{0}^{2}(1+\alpha \Delta \mathrm{T})\right\}^{2}=2 \mathrm{I}_{0}^{2}, \therefore 1+2 \alpha \Delta \mathrm{T}=2 \therefore \Delta \mathrm{T}=\frac{1}{2 \alpha}$

Hence, the correct answer is option: 'B'.

Relevant Questions