Physics - Rotation Question with Solution | TestHub

A horizontal frictionless thin rod wearing a sleeve of mass $m$ is being rotated at a constant angular velocity $\omega$ about a stationary vertical axis through one of its ends. The sleeve is held stationary with respect to the rod at a distance $r=r_1$ from the axis with the help of a light cord as shown in the figure. At some instant of time, the cord is cut. Find work done by the external agency in maintaining the angular velocity of the rod constant until the sleeve slides to a distance $r=r_2$.

(Take : $m=0.5\mathrm{kg},\omega =2\mathrm{rad}/\sec$, ${\mathrm{r}}_1=1\mathrm{m},{\mathrm{r}}_2=2\mathrm{m}$ )