If the radius of Earth is 6000 km, what will be the weight of 120 kg body (in kg Wt.) if  taken to a height of 2000 km above sea level (i.e., surface of the Earth).

With usual notation, R = 6000 km, h = 2000 km

If g and g_h denote the values of acceleration due to gravity on the surface and at a height h, then

$\frac{{\mathrm{g}}_{\mathrm{h}}}{\mathrm{g}}=\frac{{\mathrm{R}}^2}{(\mathrm{R}+\mathrm{h}{)}^2}=\frac{(6000{)}^2}{(6000+2000{)}^2}=\frac{36\times {10}^6}{64\times {10}^6}\text{ or }\frac{{\mathrm{g}}_{\mathrm{h}}}{\mathrm{g}}=\frac{9}{16}$

Thus, the weight at a height of 2000 km

        $=\left(\frac{9}{16}\right)(120 \mathrm{kg})=67.5 \mathrm{kgwt}$