State whether the following statements are true or false:
$(a)$ $G$ is a vector quantity.
$(b)$ The relation $g = \frac{GM}{r^2}$ holds well for all celestial bodies.
$(c)$ If the Earth suddenly stops rotating,the value of acceleration due to gravity at the equator will decrease.

(A) False. $G$ (Universal Gravitational Constant) is a scalar quantity.
$(b)$ True. The formula $g = \frac{GM}{r^2}$ is derived from Newton's Law of Gravitation and is applicable to all spherical celestial bodies.
$(c)$ False. The effective acceleration due to gravity at the equator is given by $g' = g - R\omega^2$. If the Earth stops rotating,$\omega = 0$,so $g' = g$. Since $g > (g - R\omega^2)$,the value of $g$ at the equator will actually increase.