Question

calculate the value of acceleration due to gravity at the place 3200 km above the Earth's surface​

Answer 1

Answer:

height above earth's surface, h = 3200 km

let radius of earth = R

thus according to the following expression for acceleration due to gravity.

g = GM/R2 at the surface of earth    -1

at height h, distance between this point and the center of earth, H = 3200 + R

4g/9 = GM/H2                               -2

thus dividing equation 1 and 2

 

4/9 = (R/H)2

or 4/9 = (R/(3200 + R))2

Answer 2

Answer:

$acceleration \: \: due \: to \: gravity \: above \: 3200km \: \\ = g \times ( { \frac{r}{r + h} )}^{2} \\ \\ = g \times {( \frac{6400}{6400 + 3200} )}^{2} \\ \\ = g \times {( \frac{6400}{9600} )}^{2} \\ \\ = g \times \frac{4}{9} \\ \\ = \frac{4}{9} g$