(2016 - I)
Solution:
Potential $V = -\frac{GM}{r} = -5.4 \times 10^{7}$ and $g = \frac{GM}{r^{2}} = 6.0$. Dividing $|V|$ by $g$ gives $r = 9000 \text{ km}$. Height $h = r - R = 9000 - 6400 = 2600 \text{ km}$.
At what height from the surface of earth the gravitation potential and the value of $g$ are $-5.4 \times 10^{7} \text{ J kg}^{-1}$ and $6.0 \text{ ms}^{-2}$ respectively. Take the radius of earth as $6400 \text{ km}$:
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