Given that the radius of the Earth and acceleration due to gravity on the surface of the Earth as 6400 km and `9.8 ms^(-2)`, respectively, find the acceleration due to gravity at a height of 5 km from the surface of the Earth.

Explanation

Given acceleration due to gravity on the surface of Earth, `g_(0) = 9.8 ms^(-2)`
radius of the Earth, r = 6400 km.
Height, h = 5 km
Here h `lt lt` R, `therefore` acceleration due to gravity at a height from the surface of the Earth
`" "g = g_(0)(1-(2h)/(R)) = 9.8(1 - (2 xx 5)/(6400)) = 9.8 (639)/(640) = 9.785 ms^(-2)`