Question

A small body of mass $m$ hangs at one end of a string of length $a$, the other end of which is fixed. It is given a horizontal velocity $u$ at its lowest position so that the string would just becomes slack, when it makes an angle of ${60}^o$ with the upward drawn vertical line. Find the tension in the string at point of projection.

Answer 1

There are two forces which are acting on the body tension on the string and the weight mg

$T=m{v}^2+mg\cos \theta$

By substituting the velocity as follows,

$v^2=u^2-2ag\left(1-\cos \theta \right)$

We get the tension as

$T=\frac{m{u}^2}{a-mg\left(2-3\cos \theta \right)}$

At $\theta ={60}^{\circ }$the tension in the string becomes negligible.

Hence we get

$u=\sqrt{\frac{ag}{2}}$

The tension at the initial point of the projection is at $\theta =0^{\circ }$

$T=\frac{3mg}{2}$