Question

A particle weigh 120N on earth surface. At what height above the earth surface will it's weight be 30N? (radius of earth=6400km)

Answer 1

Weight at Earth’s surface = W = 120 N
Weight at a height h from Earth’s surface = W’ = 30 N

W and W’ are related as
W’ = W [R / (R + h)]^2
W’ / W = [R / (R + h)]^2
30 / 120 = [R / (R + h)]^2
1/2 = R / (R + h)
R + h = 2R
h = R

∴ It’s weight will be 30 N at a height equal to radius of Earth (R)