Question

derive an eqution of potential engery

Answer 1

The energy possessed by a by a body or a system on account of its position and configuration is called potential energy or P.E.
E.g: Energy possessed by water stored in a dam, in wound spring of watch.
Suppose that body of a mass 'm' be raised to some height 'h' against 'g'. Force which is equal to the weight of the body 'mg', where g is acceleration due to gravity.
As the applied force and the displacement of the body are in the same direction.
                            Work = Force x displacement
                                  
                                   W = mg x h

                        Therefore, W = mgh

         This work is stored as the Potential energy in the body.         
This is an expression for Gravitational potential energy of a body, raised to some height above the earth's surface.