Question

If a person goes to a height equal to radius of earth from its surface, what would be his weight relative to that on the earth?

Answer 1

At the surface of earth, weight

w = mg = \(\frac{GMm}{R^2}\)

At height,  h = R,

weight, w ′ = mg′

= \(\frac{GMm}{(R+h)^2}=\frac{GMm}{(R+R)^2}\)

\(\therefore\) \(\frac{w'}{w}=\frac{R^2}{(2R)^2}\) = \(\frac{1}{4}\)

or w' = \(\frac{w}{4}\)

It means the weight would reduce to one-fourth of the weight on the surface of earth.