The height at which the weight of a body becomes one third of its weight on the surface of earth is (R is the radius of earth)
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Logic Tip: Do not use the approximation formula $g_h = g(1 - 2h/R)$ unless $h$ is specifically stated to be very small compared to $R$ (typically $< 5%$). Since the weight changes by a massive factor (1/3), the exact formula must be used.