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A simple pendulum is constructed by atta...

A simple pendulum is constructed by attaching a bob of mass m to a string of length L fixed at its upper end. The bob oscillates in a vertical circle. It is found that the speed of the bob is v when the string makes an angle `theta` with the vertical. Find the tension in the string at this instant.

Text Solution

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The forces acting on te bob asre ure
. The tension T
b. the weight mg.

As the bob moves in a vertical circle with centre at O, the radial accelertion is `v^2/L` towards O. Taking the components alogn this radius and applying Newton's second law we get
`T-mgcostheta=mv^2/L`
or, `T=m(gcostheta+v^2/L)`.
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