A simple pendulum is constructed by attaching a bob of mas 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.

Explanation

a. The forces acting on the bob are
i. the tension `T`
ii. The weight `mg`
As the bob moves in a circls of radius `L` with center at O,A centripetal force of magnitude `mv^(2)//L` is required toward o.
This force will be provided by the resitant of `T` and `mg cos alpha`

Thus `T - mg cos theta = (mv^(2))/(L)`
`T = m(g cos alpha + (v^(2))/(L))`
ii. `a_("net") = sqrt(a_(1)^(2) + a_(1)^(2)) = sqrt((g^(2) sin alpha)^(2) + ((v^(2))/(l))^(2))`
`|barF_("net")| = ma_("net") = m sqrt(g^(2) sin^(2) alpha + (v^(4))/(L^(2))`