Question

The earth is not a perfect sphere, its radius is not the same everywhere if so, will the value of $g$ be the same everywhere on earth?

Answer 1

Hint: The acceleration due to gravity, $g$ is the acceleration of the body falling under free fall within vacuum. It is considered at the surface of the earth. The value of the acceleration due to gravity is \[9.8{\text{ }}m{s^{ - 2}}\] at the surface of the earth. This is the steady gain in the velocity caused exclusively by the force of gravitational attraction.

Complete answer:
The earth appears to be round and throughout considered as a sphere. It appears to be round when viewed from the vantage point of space, it is actually closer to an ellipsoid.However even the word ellipsoid does not adequately describe the Earth’s unique and irregular shape. The radius of the earth varies from place to place. It is different at equators and the poles.

The acceleration caused by the combination of gravitational attraction and centrifugal force of the earth is coined as the gravity of the earth. $G$, is inversely proportional to the square of the radius of the earth. So as the radius of the earth increases from the poles to the equator, the value of the acceleration due to gravity, $g$ becomes greater at the poles than at the equator.
So, we can say that as the earth is not a perfect sphere and its radius is not the same everywhere the value of the acceleration due to gravity is not that same everywhere.

Note: The measurement and analysis of the rate of acceleration due to gravity is known as gravimetry. The standard value of gravitational acceleration at sea level on the earth is termed as standard gravity. As the earth is considered an ellipsoid the radius of the earth is different at the pole and the equator.