The value of the quantity $G$ in the law of gravitation:

$(i)$ Is the acceleration due to gravity of earth '$g$' always a constant at every place? Discuss.
$(ii)$ During a free fall,will heavier objects accelerate more than lighter ones? Give reason for your answer.

An apple falls from a tree because of gravitational attraction between the earth and the apple. If $F_1$ is the magnitude of force exerted by the earth on the apple and $F_2$ is the magnitude of force exerted by the apple on the earth,then:

An object is thrown vertically upwards and rises to a height of $10 \, m$. Calculate:
$(i)$ the velocity with which the object was thrown upward and
$(ii)$ the time taken by the object to reach the highest point.

List in tabular form any three differences between $g$ and $G$.

Give a reason for the statement that the value of $g$ is greater at the poles than at the equator.