Question

How does g vary with height above the surface of the earth?

Answer 1

Hint: We all know that g represents the acceleration due to gravity. It is directly proportional to the force F exerted by the earth on an object and inversely proportional to the object's mass of the object m. Change in the physical quantities representing this value will result in a change in this quantity's value.

Complete step by step answer:
We know that that the formula for gravity at a height h above the surface of the earth is given by:
$g_h=g\left(1-{\displaystyle \frac{2h}{R}}\right)$
Here $g_h$ is the acceleration due to gravity at height h above the earth's surface, g is the acceleration due to gravity at the earth's surface, h is the height from earth's surface, and R is the radius of the planet earth.
So we can say that as we move upwards, then h increases, and since it is associated with a negative sign, the value of $g_h$ decreases and becomes less than g.
Therefore gravity varies with height $g_h=g\left(1-{\displaystyle \frac{2h}{R}}\right)$, and it decreases as we move above the surface of the earth.

Additional Information:
 The height above the earth's surface has been selected to find gravity at that same height from the surface. The relation is useful in finding the value of gravity at that level exerted by any object that has been taken as an object. If we consider a depth inside the earth's surface then, we will find gravity there, but the difference will be the slight change in the value calculated by the given formula. Here, h << R because we are taking the height of an object above the earth's surface to be significantly less than the planet's radius.

Note: The value of g is maximum at the earth's surface and decreases with an increase in height h and decrease in-depth d. The value of g is affected by other factors, like the rotation of the earth, non-uniformity of earth, and earth's nonsphericity.