Question

Explain why the value of $g$ differs while moving from poles to the equator on the surface of the earth. State how would its value change on moving towards the center of the earth.

Answer 1

Acceleration due to gravity:

1. Acceleration due to gravity ($g$) varies from place to place.
2. Formula to calculate $g$ at a place is given by $\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$ , where $G$ is the Gravitational constant, $M$ is the mass of earth, $R$ is the distance from the center of the earth. Both $G$ and $M$ are constant.
3. As, $\mathrm{g}\mathrm{\alpha }\frac{1}{{\mathrm{R}}^2}$ which implies as the distance from the center of the earth increases, acceleration due to gravity decreases.
4. Earth is not a perfect sphere in shape and it bulges at the equator. Distance from the center of the earth at the equator is greater than that at the poles therefore acceleration due to gravity is less at equators and more at poles.
5. Also, $\mathrm{g}\propto M$ which implies as the mass of the earth increases, acceleration due to gravity increases.
6. As the depth increases the mass of the earth decreases, due to which the value of acceleration due to gravity decreases

Hence, on moving towards the center of the earth value of $g$ will decrease.