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  4. A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle θ with the vertical and the bob of mass m moves with a speed v is (g is the gravitational acceleration

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Q. A simple pendulum of length $L$ swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed $v$ is ($g$ is the gravitational acceleration

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Solution:

The situation is given below
image
For motion along a vertical circular track, the required centripetal force is along the radius and towards the centre of the circle is given by
$T-m g \cos \theta =\frac{m v^{2}}{L}$
$\Rightarrow T =\frac{m v^{2}}{L}+m g \cos \theta$