It is our daily life experience that an object projected upward comes back to the ground after rising to a certain height. This is due to the force of gravity acting downward. With increased initial velocity, the object rises to the greater height before coming back. If we go on increasing the initial velocity of the object, a stage comes when it will not return to the ground. It will escape out of the influence of gravity. The initial velocity of an object with which it goes out of the earth’s gravitational field, is known as escape velocity.
The escape velocity corresponds to the initial kinetic energy gained by the body, which carries it to an infinite distance from the surface of earth.
We know that the work done in lifting a body from Earth’s surface to an infinite distance is equal to the increase in its potential energy.
Where M and R are the mass and radius of the Earth respectively. The body will escape out of the gravitational field if the initial K.E. of the body is equal to the increase in P.E. of the body in lifting it up to infinity. Then