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  • A light rope is wound around a solid cylinder of mass '  ' and radius ' <img alt="r" src="https://entrancecor

A light rope is wound around a solid cylinder of mass ' m ' and radius ' r '. The rope is pulled with a force ' F '. Then The angular velocity of the cylinder at any given time ' t ' can be expressed as. (Assume, initially cylinder was at rest)

Option: 1

\left(\frac{F}{m r}\right)t


Option: 2

\left(\frac{2 F}{m r}\right)t


Option: 3

\left(\frac{m r}{F}\right)t


Option: 4

\left(\frac{2 m r}{F}\right) t


Answers (1)

best_answer

Calculating torque of all the force about centre of mass

    \begin{aligned} \tau & =F r \\ I \alpha & =F r \\ \alpha & =\frac{F r}{I} \\ \omega & =\omega_0+\alpha t=0+\left(\frac{F r}{I}\right) t \\ \omega & =\left(\frac{F r}{\frac{1}{2} mr^2}\right)t=\left(\frac{2 F}{m r}\right) t \end{aligned}

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jitender.kumar

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