Question

A string is wrapped around a cylinder of mass $M$ and radius $R$. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string, The work done on the cylinder for reaching an angular speed $\omega$ is:

• A. $\frac{2M{R}^2{\omega }^2}{3}$
• B. $\frac{M{R}^2{\omega }^2}{3}$
• C. $\frac{M{R}^2{\omega }^2}{2}$
• D. $\frac{M{R}^2{\omega }^2}{4}$

Answer 1

The correct option is D $\frac{M{R}^2{\omega }^2}{4}$

Work done is the rotational KE acquired be cylinder,

$=\frac{1}{2}I{\omega }^2$

$=\frac{1}{2}\frac{M{R}^2}{2}{\omega }^2$

$=\frac{M{R}^2}{4}{\omega }^2.$

Hence, the answer is $\frac{M{R}^2}{4}{\omega }^2.$