Question

A uniform cylindrical rod of mass m and length L is rotating with an angular velocity $\omega.$ The axis of rotation is $\bot$ to its axis of symmatry and passes through one of its edge faces . If the room temperature increases by 't' and the coefficient of linear expansion is $\alpha,$ the change in its angular velocity is

• A. $2\omega\alpha\,t$
• B. $\omega\alpha\,t$
• C. $\frac{3}{2}\omega\alpha\,t$
• D. $\frac{\omega\alpha\,t}{2}$

Answer 1

Answer: (A)

As no external torque is acting on the rod, its angular momentum about the axis of rotation should remain constant .
$\Rightarrow $ $I \omega = I^1 \omega^1$
$I = \frac{ ML^2}{3} $ and $I^1 = \frac{ML^2}{3}$
$\therefore \, L^2 \omega = L^2 \, \omega^1$
here $L^1 = L(1 + \propto t)$
$\therefore $ $\omega^1 = \frac{ \omega}{(1 + \propto t)^2} = \omega(1 - 2 \propto t)$
$\therefore $ change in angular speed $\Delta \omega = 2 \propto \omega t$