Calculate the force of gravitation between two objects of masses $10 \; kg$ and $20 \; kg$ at a distance of $10 \; m$ from each other. $\left[G = 6.67 \times 10^{-11} \; Nm^2 kg^{-2}\right]$

The equation $F = G \frac{m_1 m_2}{r^2}$ is valid only for:

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

Show mathematically that the acceleration experienced by an object during free fall is independent of the mass of the object.

$(i)$ 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. $(G = 6.7 \times 10^{-11} \, Nm^{2} kg^{-2})$

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