A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle `alpha`. A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in figure. The maximum angle `theta` which the string makes with the vertical after hitting the pin is

Options

A. (a) `cos^-1[(Lcosalpha+l)/(L+l)]`
B. (b) `cos^-1[(Lcosalpha+l)/(L-l)]`
C. (c) `cos^-1[(Lcosalpha-1)/(L-l)]`
D. (d) `cos^-1[(Lcosalpha-1)/(L+l)]`

Answer

C

Explanation

Since the pendulum started with no kinetic energy, conservation of energy implies that the potential energy at `Q_(max)` must be equal to the original potential energy, i.e., the vertical position will be same. Therefore,
`Lcos alpha=l+(L-l)cos theta`
`implies cos theta=(Lcos alpha-1)/(L-1)`
`impliestheta=cos^-1[(Lcos alpha-1)/(L-1)]`