Question

A body weighs $80\text{N}$ on the surface of the earth. What is its weight at a height equal to radius of the earth?

• A. $40\text{N}$
• B. $60\text{N}$
• C. $30\text{N}$
• D. $20\text{N}$

Answer 1

The correct option is D $20\text{N}$

Acceleration due to gravity at height $h$ above the surface of earth is given by,

$g^{\prime }=\frac{g{R}^2}{(R+h{)}^2}$

$\Rightarrow m{g}^{\prime }=\frac{mg{R}^2}{(R+h{)}^2}$

$m{g}^{\prime }=\frac{mg{R}^2}{(2R{)}^2}$

$m{g}^{\prime }=\frac{mg}{4}$

$=\frac{80}{4}$

$=20\text{N}$