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.

Acceleration due to gravity at the surface of a planet is equal to that at the surface of the Earth,and its density is $1.5$ times that of the Earth. If the radius of the Earth is $R$,the radius of the planet is:

In order to make the effective acceleration due to gravity equal to zero at the equator,the angular velocity of rotation of the earth about its axis should be $(g = 10\,m/s^2$ and radius of earth is $6400\,km)$.

How much is the radius of the Earth at the equator greater than the radius at the poles?

Different planets have masses $M_1, M_2, M_3$ and radii $R_1, R_2, R_3$ respectively. The acceleration due to gravity on their surfaces are $g_1, g_2, g_3$ respectively. Based on the given graph,arrange their masses in descending order.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A):$ Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason $(R):$ Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements,choose the most appropriate answer from the options given below: