Question

Where the centre of gravity of the atmosphere does lie?

Answer 1

Hint: Think of the Earth as a spherical ball. Also think about what shape the atmosphere with the Earth resembles. If you can think about the correct shape, it is very easy to deduce the centre of mass since in most cases of uniform mass distribution it is the geometric centre.

Complete answer:
The atmosphere forms a blanket around us. Although the density of air decreases as we go up, at the same level the density is the same in every point on the surface of the Earth. Thus the atmosphere can be said to form a spherical shell with some thickness and an inner cavity covering the whole of Earth. The inner cavity is where the Earth is located. For such a spherical shell the centre of gravity lies at the geometric centre.

Thus the atmosphere’s centre will be the centre of the shell (here it is in regards to the atmosphere) and thus it will coincide with the centre of the inner spherical cavity (here it is in regards to Earth)

Hence we can say that the centre of gravity of the whole atmosphere is the centre of the Earth.

Note: See that the value of gravity will remain the same at the same level of atmosphere all over the world. Thus it uniformly changes for the same rate at every place. This is the reason we can say that the center of gravity of the atmosphere is at the center of Earth.