Gravitation Question 7
Question 7 - 2024 (30 Jan Shift 1)
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 $6400 \mathrm{~km}$. The height of this point above the earth’s surface is :
(1) $1600 \mathrm{~km}$
(2) $540 \mathrm{~km}$
(3) $1200 \mathrm{~km}$
(4) $1000 \mathrm{~km}$
Show Answer
Answer: (1)
Solution:
$-\frac{G M_{E}}{R_{E}+h}=-5.12 \times 10^{-7}$.
$\frac{G M_{E}}{\left(R_{E}+h\right)^{2}}=6.4 \ldots$
By (i) and (ii)
$\Rightarrow h=16 \times 10^{5} \mathrm{~m}=1600 \mathrm{~km}$
