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Answer: (c) 4684.8 km

At height \(h\) above the surface, \(g_h = g\dfrac{R^{2}}{(R+h)^{2}}\). The weight becomes one-third when

\[\frac{R^{2}}{(R+h)^{2}} = \frac{1}{3}\ \Rightarrow\ \frac{R+h}{R} = \sqrt3\]

\[h = (\sqrt3 - 1)R = 0.732R\]

With \(R = 6400\ \mathrm{km}\):

\[h = 0.732\times6400 = 4684.8\ \mathrm{km}\]

(The approximation \(g_h \approx g(1 - 2h/R)\) cannot be used here, because it is valid only for \(h \ll R\).)

Doubtly AI · 23 Oct 2026 AI-verified · Oct 2026 Report
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