Question

A body is released at a distance far away from the surface of the earth. Calculate its speed when it is near the surface of earth. Given $g=9.8m{s}^{-2}$, radius of earth $R=6.37\times {10}^6$m.

• A. $22\times {10}^{3}m{s}^{-1}$.
• B. $11.2\times {10}^{3}m{s}^{-1}$.
• C. $23\times {10}^{3}m{s}^{-1}$.
• D. $10\times {10}^{3}m{s}^{-1}$.

Answer 1

The correct option is B $11.2\times {10}^{3}m{s}^{-1}$.

Conservation of energy implies
$0+0=\frac{1}{2}m{v}^2-\frac{GMm}{R}$
$v=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2\left(R^{2}g\right)}{R}}$
$=\sqrt{2Rg}\approx 11.2\times {10}^{3}m{s}^{-1}$.