Question

A light in extensible string is wrapped around a cylinder of mass m and radius R. The string is pulled vertically upwards to prevent the center of mass from falling as the cylinder unwinds the string. The length of the string unwound when the cylinder has reached a speed $\omega$ will be

• A. $\frac{R\omega }{4g}$
• B. $\frac{R^2{\omega }^2}{4g}$
• C. $\frac{R\omega }{8g}$
• D. $\frac{R^2{\omega }^2}{8g}$

Answer 1

The correct option is B $\frac{R^2{\omega }^2}{4g}$

$\begin{array}{c}T=mg\\ mg\cdot R=\frac{m{R}^2}{2}\cdot \alpha \\ \alpha =2g\\ \&v=wR\\ Now,\\ v^2=2as\\ \Rightarrow S=\frac{w^2{R}^2}{2\cdot 2g}=\frac{w^2{R}^2}{4g}\\ Hence,optionBiscorrectanswer.\end{array}$