Gravitation Question 7
Question 7 - 2024 (30 Jan Shift 1)
The gravitational potential at a point above the surface of earth is $-5.12 \times 10^{7} J / kg$ and the acceleration due to gravity at that point is $6.4 m / s^{2}$. Assume that the mean radius of earth to be $6400 km$. The height of this point above the earth’s surface is :
(1) $1600 km$
(2) $540 km$
(3) $1200 km$
(4) $1000 km$
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)
$\Rightarrow h=16 \times 10^{5} m=1600 km$
