The intial configuration of the system is as shown in the figure.

The string and the pulley are light. The bob is released and the string starts wrapping around the pulley. (The pulley is held in place by a force applied at the centre)

Find the rate r at which the length of the string warpped around the pulley increaes (as a function of `theta`).

Options

A. `r=(R)/((l-Rtheta))sqrt([2g(l-Rtheta)sin theta])`
B. `r=(R)/((l-Rtheta))sqrt(2g[(l-Rtheta)sin theta+R cos theta])`
C. `r=(R)/((l-Rtheta))sqrt(2g[(l-Rtheta)sin theta+R(1-sin theta)])`
D. `r=R)/((l-Rtheta))sqrt(2g[(l-Rtheta)sin theta+R(1-cos theta)])`

Answer

D