Question

Given that mass of earth is $M$ and its radius $R$. body is dropped from a height equal to the radius of the earth above the surface of the earth. When it reaches the ground velocity of body will be

• A. $\frac{GM}{R}$
• B. ${\left(\frac{GM}{R}\right)}^{1/2}$
• C. $\frac{2GM}{R}$
• D. ${\left(\frac{2GM}{R}\right)}^{1/2}$

Answer 1

The correct option is B ${\left(\frac{GM}{R}\right)}^{1/2}$

This question can be very easily tackled using conservation of energy with a bit care,

Total energy of body at height 2R = $m_b\frac{G{M}_e}{4R_e^2}2R$=Total energy of body at surface of earth=$\frac{m_b{v}^2}{2}$

From these equations we get v=$[\frac{G{M}_e}{R_e}{]}^{\frac{1}{2}}$