Explanation:
With usual notation, \(R=6000 {~km}, h=2000 {~km}\)
If \(g\) and \({{\rm{g}}_h}\), denote the values of acceleration due to gravity on the surface and at a height \(h\),then
\(\frac{{{g_h}}}{g} = \frac{{{R^2}}}{{{{(R + h)}^2}}} = \frac{{{{(6000)}^2}}}{{{{(6000 + 2000)}^2}}}\)
\( = \frac{{36 \times {{10}^6}}}{{64 \times {{10}^6}}}{\rm{ or }}\,\,\frac{{{g_h}}}{g} = \frac{9}{{16}}\)
Thus, the weight at a height of 2000 km
\(=\left(\dfrac{9}{16}\right)(120 {~kg})=67.5 {~kg}\,\,\ {wt}\)