Question

a bob tied to a string is whirled along a vertical circle then what is the tension in the string

Answer 1

At the extreme point, velocity of the bob is zero. Therefore the bob can be considered to be at rest for a moment.

The weight of the body can be resolved in to two diections as shown.

From the vector diagram it can be seen that the component of weight along the length of the string is mgcosθmgcosθ  and normal to the string is mgsinθmgsinθ.

As there is no motion in the direction of the string, the forces along the direction of the string must be in equilibrium.

Forces along that direction are the component of weight, mgcosθmgcosθ and the tension TT in the string.

For equilibrium, tension T=mgcosθ

Hope this helps.