Question

If g on the surface of the earth is 9.8 m / s 2 then its value at a height of 6400 km is

Answer 1

So at height 6400km from surface of earth value of g = 2.45 m/s²

Answer 2

Value of g on an height 6400km from earth is 2.45m/sec^2

We know that  real formula from newton's law of gravity is

F=mg=GmM/r^2

So g=GM/r^2-----------equation 1

Where r is the radius of earth

G is the universal gravitational constant

M is the mass of earth

So for a distance at height h above earth the formula becomes

gh=GM/(r+h)^2

We know radius of earth =6400km and h=6400km hence h=r

gh=GM/(r+r)^2

gh=GM/4r^2

from equation 1 we have:-------

gh=g/4 g=9.8m/s^2

So gh=9.8/4=2.45m/sec^2