The mass of a man on the earth is $100\, kg$. Does his weight on the moon increase or decrease?

State whether the following statement is True or False:
The centre of mass and centre of gravity for a small body lie at the same point.

When dropped from the same height,a body reaches the ground quicker at the poles than at the equator. Why?

Suppose the gravity of the $Earth$ suddenly becomes zero,then in which direction will the $Moon$ begin to move if no other celestial body affects it?

Why is the value of $g$ greater at the poles than at the equator?

$(i)$ How is the force of attraction dependent on the masses of objects and the distance between them?
$(ii)$ The mass of the Earth is $6 \times 10^{24} \, kg$ and that of a natural satellite is $6.5 \times 10^{20} \, kg$. If the distance between them is $3.35 \times 10^{6} \, km$, calculate the force exerted by the Earth on it. $(G = 6.7 \times 10^{-11} \, Nm^{2} kg^{-2})$