Question

Give the definition of escape velocity. Obtain the expression for escape velocity from earth’s surface.

Answer 1

The minimum velocity of projection of the object for which it escapes i.e., it leaves the gravitational field of the earth forever and never returns back, is called the escape velocity. It is denoted by U. When an object is projected vertically from earth’s surface, then its kinetic energy goes on decreasing and potential energy goes an increasing, when complete kinetic energy is converted into the potential energy, from there the object returns back to earth’s surface. Thus, if the object is given kinetic energy equal to magnitude of gravitational, energy, the object will reach to infinity i.e., it will escape.
Hence,
Escape energy = |Gravitational potential energy|

Escape Velocity on the Earth Surface:
∴ g = 9.8 ms^-2
∴ Re = 6400 km = 64 x 10⁶ m;

∴ v_e = \(\sqrt{2\times9.8\times6.4\times10^6}\)

or v_e = 11.2 kms^-1

Escape Velocity on Moon:
For moon, g_m = 1.63 ms^-2;
R_m = 1.74 x 10⁶ m
∴ v_e on moon = \(\sqrt{2\times1.63\times1.76\times10^6}\)

= 2.3 kms^-1