Question

At a point above the surface of the earth, the gravitational potential is $-5.12\times 10^{7}Jk{g}^{-1}$ and the acceleration due to gravity is $6.4m{s}^{-2}$ . Assuming the mean radius of the earth to be $6400km$ , the height of this point above the earth's surface is.

• A. $1400km$
• B. $1500km$
• C. $1600km$
• D. $1700km$

Answer 1

Answer: (C)

Let $r$ be the distance of the given point from the centre of the earth. Then Gravitational potential $=-\frac{GM}{r}=-5.12\times {\left(10\right)}^7...\left(i\right)$
And acceleration due to gravity, $g=\frac{GM}{r^2}=\mathrm{6.4...}\left(ii\right)$
Dividing Eq. $(i)$ by Eq. $(ii)$ , we get $r=\frac{5.12\times 10^7}{6.4}$
$=8\times 10^{6}m$
$=6000km$
$\therefore$ Height of the point from earth's surface $=r-R=8000-6400$
$=1600km$