Question

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

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

Answer 1

The correct option is B $\sqrt{\frac{2G{M}_e}{R}}$

$\frac{1}{2}{mV}_1^2=\frac{-GMm}{2R}+\frac{GMm}{R}$

$\Rightarrow \frac{1}{2}{mV}_1^2=\frac{GMm}{R}$

$\Rightarrow V_1^2=\frac{2GM}{R}$

$V_1=\sqrt{\frac{2GM}{R}}$