The bob of a simple pendulum having length l | vedclass

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(C) When the bob is displaced by an angle $	heta$,it rises to a vertical height $h$ above its mean position.By the law of conservation of mechanical

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$\sqrt{2gl(1 - \cos 	heta)}$

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(C) When the bob is displaced by an angle $	heta$,it rises to a vertical height $h$ above its mean position.By the law of conservation of mechanical energy,the potential energy at the extreme position is converted into kinetic energy at the mean (lowest) position.$mgh = \frac{1}{2}mv_{\max}^2$$v_{\max} = \sqrt{2gh}$From the geometry of the pendulum,the vertical distance from the point of suspension to the bob at the extreme position is $l \cos 	heta$.Therefore,the height $h$ is given by:$h = l - l \cos 	heta = l(1 - \cos 	heta)$Substituting the value of $h$ into the velocity equation:$v_{\max} = \sqrt{2gl(1 - \cos 	heta)}$

The bob of a simple pendulum having length $l$ is displaced from the mean position to an angular position $\theta$ with respect to the vertical. If it is released,then the velocity of the bob at the lowest position is:

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