question_answer

A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is:                        [AIPMT 2001]

A) \[\sqrt{\frac{GM}{R}}\]

B) \[\sqrt{\frac{2GM}{R}}\]

C) \[\sqrt{\frac{5}{4}\,\frac{GM}{R}}\]

D) \[\sqrt{\frac{3GM}{R}}\]

Correct Answer: A

Solution :

Key Idea: According to the conservation of energy, total energy at the surface of earth must equal to the total energy at the maximum height.

As from key idea, energy at surface of earth = energy at maximum height

or

or

or

Alternative: The expression for the speed with which a body should be projected so as to reach a height h is

Here,  (given)