Escape Velocity

Escape velocity is defined as the velocity with which a body must be thrown vertically upwards in order that it may just escape the gravitational pull of earth.

When we throw a body vertically upwards with certain velocity, the body retuns to the earth's surface after some time. However, when the body is thrown with a velocity equal to the escape velocity, the body overcomes the earth's gravitational pull and also the resistance of the earth's atmosphere. The body never returns to the surface of earth again.

Expression of Escape Velocity

 Escape Velocity

Consider a body of mass m lying at a distance x from the centre of earth. Let M be the mass of earth. According to Newton 's law of gravitation, the gravitational force F of attraction between the body and earth is given by

Let Ve be the escape Velocity, then kinetic energy imparted to the body

Therefore,

 Escape Velocity
Here, x is the radius of earth.

Substituting values we get Escape Velocity from the earth's surface i.e. 11.2 km/s-1.