Question

Derive expression of escape velocity...

Answer 1

this is the expression for escape velocity

Answer 2

Derivation of Escape Velocity



Suppose that the planet be a perfect sphere of radius R having mass M. Let a body of mass m is to be projected from point A on the earth's surface as shown in the figure. Join OA and produce it further. Let us take two points P and Q which are at distances x and (x + dx) from the center of the earth.

To calculate the escape velocity of the earth, let the minimum velocity to escape from the earth's surface be ve. Then, kinetic energy of the object of mass m is



When the projected object is at point P which is at a distance x from the center of the earth, the force of gravity between the object and earth is



Work done in taking the body against gravitational attraction from P to Q is given by