CBSE Class 11-science Answered

Escape velocity is the velocity required to be given to the object so that

the object is moved far away from earth's gravitational field .

Let v_e be the escape velocity given to the object

Total energy E of the object on earth surface is sum of its kinetic energy and potential energy .

...............................(1)

First term in above expression is kinetic energy and second term is potential energy

m is mass of object , G is universal gravitational constant , M is mass of earth and R is radius of earth.

When the object is noved to infinite distance far away from earth;s gravitatioal field ,

its potential energy is zero and it has negligible kinetic energy .

hence we can consider total energy E_∞ at infinite distance is zero.

By conservation of energy

E = E_∞ = 0

Hence , from eqn.(1) , we get

by substituting g = 9.8 m /s²  and  radius of earth R = 6371 km = 6.371 m , we get

v_e = 11.2 km/s