Question

A body attains a height equal to the radius of the earth when projected from earth' surface. The velocity of the body with which it was projected is.

• A. $\sqrt{\frac{GM}{R}}$
• B. $\sqrt{\frac{2GM}{R}}$
• C. $\sqrt{\frac{5}{4}\frac{GM}{R}}$
• D. $\sqrt{\frac{3GM}{R}}$

Answer 1

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

Let the velocity with which it was projected be $v$.At height $h$, velocity is zero.

Applying conservation of energy at the surface and at a height $h=R$,

$(K.E{)}_R+(P.E{)}_R=(K.E{)}_{2R}+(P.E{)}_{2R}$

$\frac{1}{2}m{v}^2+(-\frac{GMm}{R})=0+(-\frac{GMm}{2R})$

$⟹v=\sqrt{\frac{GM}{R}}$