The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is : [Radius of earth $R = 6400 km$ and $\sqrt{3} = 1.732$ ]

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4267 km

3840 km

4685 km

2133 km

answer is B.

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Detailed Solution

$\begin{aligned} {Mg}^{'} = \frac{M}{3} g \\ g^{'} = \frac{g}{3} \\ g^{'} = g {(\frac{R}{R + h})}^{2} = \frac{g}{3} \\ \frac{R}{R + h} = \frac{1}{\sqrt{3}} . \\ h = (\sqrt{3} - 1) R \\ = (1.732 - 1) 6400 \\ h = 4685 km \end{aligned}$

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