Question

Derive the expression of due to gravity at a point above the surface of earth

Answer 1

There is low pressure when we go up to the mountain because the oxygen gets reduces because of atmospheric pressure.

Answer 2

Answer:

Gravity at a point above the surface of earth:

$\implies \sf g=\dfrac{Gme}{Re^{2}}\\ \\ \\ \implies \sf g' = \dfrac{Gme}{(Re+h)^{2}}\\ \\ \\ \implies \sf \dfrac{g'}{g}=\dfrac{Gme}{(Re+h)^{2}}\times \dfrac{R^{2}}{Gme}\\ \\ \\ \implies \sf \dfrac{g'}{g}=\dfrac{Re^{2}}{Re^{2}\Bigg(1+\dfrac{h}{Re}\Bigg)^{2}}\\ \\ \\ \implies \sf \dfrac{g'}{g}=\Bigg(1+\dfrac{h}{Re}\Bigg)^{-2}\\ \\ \\ \implies \sf \dfrac{g'}{g}=\Bigg(1-\dfrac{2h}{Re}\Bigg)\\ \\ \\ \implies {\boxed{\sf g' = g\Bigg(1-\dfrac{2h}{Re}\Bigg)}}$

Hence, This shows that gravitation acceleration decreases above 'h' height.