Question

A circular loop of rope of length L rotates with uniform angular velocity ω about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

• A. $\omega L$
• B. $\frac{\omega L}{2\pi }$
• C. $\frac{\omega }{L}$
• D. $\frac{\omega L}{4{\pi }^2}$

Answer 1

The correct option is B $\frac{\omega L}{2\pi }$


Consider an element which makes an angle $d\theta$ at the center of loop to find the tension in the rope.
$2tsin\frac{d\theta }{2}=dm.{\omega }^{2}R2t\frac{d\theta }{2}=\frac{m}{\ell }d\theta .{\omega }^{2}RT=\frac{m{\omega }^2{R}^2}{\ell }\therefore V=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{T}{\frac{m}{l}}}=\omega R\therefore V=\frac{\omega L}{2\pi }$