Question

Calculate the h above the earth surface at which the value acceration due to gravity reduces to half of its value on earth surface​

Answer 1

According to the law of Gravitation;

F = GmM/r^2

Where: F - Force exerted on the bodies, G - Gravitational constant, m - Mass of the body, M - Mass of the Earth, r - distance between the body and the core of the Earth.

Acceleration due to gravity;

g = F/m = GM/r^2

At surface of Earth;

r = R and g = GM/R^2

Let the body be at a distance of 'h' from the surface of the Earth; R - radius of the Earth

r = R + h and g' = GM/(R+h)^2

According to the question: at height 'h': g' = g/2;

GM/2R^2 = GM/(R+h)^2

2R^2 = (R+h)^2

h = (√2 - 1)R

R = 6371 km

h = 2637 km

Thus, at a height of approximately 2637 km will the acceleration due to gravity will be half of the acceleration due to gravity on the surface!

Hope it helps....