$(a)$ Differentiate between $G$ and $g$.
$(b)$ Is the value of $g$ the same everywhere on Earth? Reason out.
$(c)$ How does the gravitational force between two objects change if the distance between them is tripled?

(A) $G$ is the Universal Gravitational Constant with a fixed value of $6.673 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}$. It remains constant everywhere in the universe.
$g$ is the acceleration due to gravity,which varies depending on the location. Its $SI$ unit is $\text{m s}^{-2}$.
$(b)$ No,the value of $g$ is not the same everywhere on Earth. The Earth is not a perfect sphere; it is flattened at the poles and bulges at the equator. Since $g = \frac{GM}{R^2}$,the radius $R$ is smaller at the poles compared to the equator. Therefore,the value of $g$ is greater at the poles and smaller at the equator.
$(c)$ According to Newton's Law of Universal Gravitation,$F = \frac{G M m}{r^2}$,so $F \propto \frac{1}{r^2}$.
If the distance $r$ is tripled $(r' = 3r)$,the new force $F'$ becomes $F' = \frac{G M m}{(3r)^2} = \frac{G M m}{9r^2} = \frac{1}{9} F$.
Thus,the gravitational force becomes one-ninth of its original value.