Question

In Figure shown, a weight $W$ is attached to string wrapped round a solid cylinder of mass m mounted on a frictionless horizontal axle at $O$. if weight starts from rest and falls through a distance $h$, then the speed at this instant will be

• A. Proportional to $R$
• B. Proportional to $\frac{1}{R}$
• C. Proportional to $\frac{1}{R^2}$
• D. Independent of $R$

Answer 1

The correct option is D Independent of $R$

The change in potential energies is given as $Wh$ and the final kinetic energy is given as $\frac{1}{2}m{v}^2+\frac{1}{2}\frac{m{r}^2}{2}\frac{v^2}{r^2}=\frac{3}{4}m{v}^2$.We equate the two energies to see that the relation is independent of r. Thus option D is correct.