The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (Given, radius of earth $R_e$ = 6400 km )

Answer (3)

Given,

Weight of a body at the surface of earth,

$W_e =mg=18N$

Radius of earth, $R_e=6400km$

Altitude, $h=3200km=\displaystyle \frac{R_e}{2}$

Also, $\displaystyle g=\frac{GM}{R_e}$

Weight of a body at an altitude of h above the earth's surface,

$\displaystyle \begin{aligned}W_h&=m\frac{GM}{(R_e+h)^2}\\&=m\frac{GM}{\Bigg(R_e+\displaystyle \frac{R_e}{2} \Bigg)^2}\ \ \ \ \ \ \ \ \ \Big(\because h=\frac{R_e}{2} \Big)\\&=m\frac{GM}{\Bigg(\displaystyle \frac{3R_e}{2}\Bigg)^2 }\\&=\frac{4}{9}mg=\frac{4}{9} \times18=8N \end{aligned}$