Question

Find the percentage decrease in the acceleration due to gravity when a body is taken from the surface of the earth to height of 32km from its surface

Answer 1

Here is your answer...

Answer 2

Answer: 1%

The acceleration due to gravity is inversely related to the distance:

⇒$\frac {g'}{g}=\frac{R^2}{(R+d)^2}$

when d is very small as compared to R, then,

$g' = g (1-\frac{2d}{R})$

where g' is the acceleration due to gravity at height d from the surface of the earth.

g = 9.81 m/s²

R = Radius of Earth = 6371 km

d = 32 km

Percentage decrease in the acceleration due to gravity:

$\frac{g-g'}{g} \times 100\%= 1- (1-\frac{2d}{R})\times 100\%= \frac{2\times 32}{6371} \times 100\% = 0.01 \times 100 \% = 1\%$