A bob of mass `m` suspended by a light inextensible string of length 'l' from a fixed point. The bob is given a speed of `sqrt(6gl)`. Find the tension in the string when string deflects through an angle `120^@` from the vertical.

Explanation

To solve the problem of finding the tension in the string when the bob deflects through an angle of \(120^\circ\) from the vertical, we will follow these steps:

### Step 1: Understand the system
We have a bob of mass \(m\) attached to a string of length \(l\). The bob is given an initial speed of \(\sqrt{6gl}\) and swings to an angle of \(120^\circ\) from the vertical.

### Step 2: Determine the conservation of mechanical energy
Since there are no non-conservative forces acting on the system (like friction), we can apply the principle of conservation of mechanical energy. The initial kinetic energy (KE) plus the initial potential energy (PE) will equal the final kinetic energy plus the final potential energy.

...