Question

At a point above the surface of the earth, the gravitational potential is $-5.12\times 10^{7}Jkg^{- 1}$ and the acceleration due to gravity is $6.4ms^{- 2}$ . 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 $=-\frac{G M}{r}=-5.12\times \left(10\right)^{7}...\left(i\right)$
And acceleration due to gravity, $g=\frac{G M}{r^{2}}=6.4...\left(i i\right)$
Dividing Eq. $\left(\right.i\left.\right)$ by Eq. $\left(\right.ii\left.\right)$ , 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 $=r-R=8000-6400$
$=1600km$