The gravitational potential at a point above the surface of earth is $-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}$ and the acceleration due to gravity at that point is $6.4 \mathrm{~m} / \mathrm{s}^2$. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is :
Select the correct option:
A
1600km
B
540km
C
1200km
D
1000km
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$
\begin{aligned}
& -\frac{G M_E}{R_E+h}=-5.12 \times 10^{-7} \\
& \frac{G M_E}{\left(R_E+h\right)^2}=6.4
\end{aligned}
$$
By (i) and (ii)
$$
\Rightarrow h=16 \times 10^5 \mathrm{~m}=1600 \mathrm{~km}
$$
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