(a) Effect of Altitude: when h is comparable with R and h << R.
g' = g\(\big(1-\frac{2h}{R}\big)\)
From these relations, we conclude that acceleration due to gravity decreases with increases in height from the surface of earth.
(i) Fractional decrease in the value of g with height = \(\frac{g-g'}{g}\) = \(\frac{2h}{R}\)
(ii) % decrease in the value of g = \(\big(\frac{g-g'}{g}\big)\)x 100 = \(\frac{2h}{R}\) x 100%
(b) Effect of depth:
(i) The acceleration due to gravity decreases with increase in depth d and becomes zero at the center of the earth.
(ii) Decrease in the value of g with depth,
\(\Delta\)g = g - g' = \(\frac{gd}{R}\)
\(\therefore\) Fractional decrease in the value of g with depth = \(\frac{g-g'}{g}\) = \(\frac{d}{R}\)
(iii) % decrease in the value of g with depth \(\frac{g-g'}{g}\) x 100 = \(\frac{d}{R}\) x 100%
