question_answer

The, earth is assumed to be a sphere of radius R, A platform is arranged at a height R from the surface of the earth.

The escape velocity of a body from this platform is \[f{{v}_{e}},\] where \[{{v}_{e}}\] is its escape velocity from the surface of the earth.

The value of f is:                              [AIPMT (S) 2006]

A) \[\sqrt{2}\]        

B) \[\frac{1}{\sqrt{2}}\]

C) \[\frac{1}{3}\]

D) \[\frac{1}{2}\]

Correct Answer: B

Solution :

Key Idea: If energy in the form of kinetic energy which is equal to binding energy, supplied to the sphere, it leaves the gravitational field of earth.

At a platform at a height h,

escape energy = binding energy of sphere

or

or

But at surface of earth,

As given,

Hence,

or