Question

A particle is kept at rest at a distance $R$ (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is

• A. $\sqrt{\frac{GM}{4R}}$
• B. $\sqrt{\frac{GM}{2R}}$
• C. $\sqrt{\frac{GM}{R}}$
• D. $\sqrt{\frac{2GM}{4R}}$

Answer 1

The correct option is C $\sqrt{\frac{GM}{R}}$

Using law of conservation of energy, we can write
$-\frac{GMm}{2R}+\frac{1}{2}m{v}^2=0$
$m{v}^2=\frac{GMm}{R}$
$v^2=\frac{GM}{R}$
$v=\sqrt{\frac{GM}{R}}$