Motion in a Vertical Circle

Consider a body of mass 'm' tied to a string and rotated in a vertical circle of radius 'r'. The velocity (speed) of the body keeps changing. It is maximum at the bottom and a minimum at the top.

Let u be the speed of the particle at the bottom

Let v be the speed at some point

By the principle of conservation of energy

Where (h is the vertical height of P above the lowest point)

Let T be the tension in the string.

Tension at the highest point is obtained by putting h = 2r in

Tension at the bottom of the circle is obtained by putting h = 0.

Tension at the highest point is given by putting h=2r

T_L - T_H = 6mg