The earth is a solid sphere of radius 6400 km, the value of acceleration due to gravity at a height 800 km above the surface of the earth is

Options

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

Answer

B

Explanation

Acceleration due to gravity at a height h from 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)/(g) xx 100% = (1 - (g_h)/(g) ) xx 100%`
` = (1- (6400/6500)^2) xx 100% = 3%`