Taking the radius of the earth to be 6400 km, by what percentage will the acceleration due to gravity at a height of 100 km from the surface of the earth differ from that on the surface of the earth

Options

A. About 1.5%
B. About 5%
C. About 8%
D. About 3%

Answer

D

Explanation

Acceleration due to gravity at a height h from the surface of the earth is
`g_h=(gR^2)/((R+h)^2)`
where g is the acceleration due to gravity on the surface of the earth and R is the radius of the earth
`g_h=g((6400)^2)/((6400+100)^2)=g((6400)/(6500))^2` ........(i)
% change in acceleration due to gravity
`=(g-g_h)/gxx100%=(1-(g_h)/g)xx100%`
`=[1-((6400)/(6500))^2]xx100%`[ Using (i)]
=3%