At a point above the surface of Earth, the gravitational potential is `-5.12 xx 10^(7) J kg^(-1)` and the acceleration due to gravity is `6.4 ms^(-2)`. Assuming the mean redius of the earth to be `6400 km`, calcualte the height of this point above the Earth's surfcae.

Explanation

Let `r` be the distance of the given point from the centre of the Earth. Then,
Gravitational potential `= - (GM)/(r )`
`= - 5.12 xx 10^(7)` ..(i)
and acceleration due to gravity,
`g = (GM)/(r^(2)) = 6.4` ..(ii)
Dividing (i) by (ii), we get
`r = (5.12 xx 10^(7))/(6.4) = 8 xx 10^(6) m = 8000 km`.
`:.` height of the point from Earth's surface
`= r - R = 8000 - 6400 = 1600 km`