Question

A body weighs $120\text{N}$ at a height equal to the radius of the Earth. Its weight on the Earth's surface will be -

• A. $140\text{N}$
• B. $72\text{N}$
• C. $390\text{N}$
• D. $480\text{N}$

Answer 1

The correct option is D $480\text{N}$

The value of acceleration due to gravity at a height $‘h^{\prime }$ from the Earth's surface is

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

$\therefore \frac{m{g}_h}{mg}={\left(\frac{R}{R+h}\right)}^2={\left(\frac{R}{R+R}\right)}^2=\frac{1}{4}$

$\Rightarrow \frac{W_h}{W_s}=\frac{1}{4}$

$\Rightarrow W_s=4\times W_h=4\times 120=480\text{N}$