A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle α . A pin is located at a distance l below the pivot point. When the pendulum swings down, t

Question

A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle α . 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 the figure. If the particle doesn't undergo a complete vertical circle, then the maximum angle θ < π 2 through which the string swings after hitting the pin is

TestHub · Accepted Answer

At the bottom most point, square of speed of bob,

$v^{2} = 2 g L (1 - c o s α)$

It will rise further to a height,

$h = \frac{v^{2}}{2 g} = L (1 - \cos α)$

or $(L - l) (1 - \cos θ) = L (1 - \cos α)$

$∴ θ = \cos^{- 1} [\frac{L \cos α - l}{L - l}]$

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