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  4. A simple pendulum has a string of length l and bob of mass m. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is :

Q. A simple pendulum has a string of length $l$ and bob of mass $m$. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is :

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Solution:

The minimum velocity that should be imparted to the bob so that it completes vertical circle is
$v=\sqrt{5 g l}$
At lowest position,
$T=m g+\frac{m v^{2}}{l} $
$T=m g+\frac{m(5 g l)}{l}$
$T=6 \,m g$

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