Write the expression for the acceleration due to gravity at the surface of the earth.

$A$ body weighs $63 \, N$ on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth (in $, N$)? (Given: Mass of the earth $= 6 \times 10^{24} \, kg$ and radius of the earth $= 6.4 \times 10^{6} \, m$)

The value of $g$ on the earth's surface is $9.8 \, m s^{-2}$. Suppose the earth suddenly shrinks to one-third of its present size without losing any mass. What is the value of $g$ on the surface of the shrunk earth (in $, m s^{-2}$)?

Define 'acceleration due to gravity of earth'. Does the acceleration produced in a freely falling body depend on the mass of the body? Justify your answer mathematically.

Prove that if a body is thrown vertically upward,the time of ascent is equal to the time of descent.

Give reason:
$(a)$ Value of '$g$' is not constant on Earth.
$(b)$ Objects with different masses take the same time to fall from a fixed height.
$(c)$ '$G$' is known as the universal gravitational constant.