$(i)$ 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.

(N/A) $(i)$ We know $g = \frac{GM}{R^2}$. Thus,on the surface of the earth and very close to the surface,'$R$' (i.e.,the radius of the earth) remains constant; hence,'$g$' will be constant. However,at distances far away from the surface of the earth,when '$R$' changes,the value of '$g$' will no longer remain constant.
$(ii)$ No,during a free fall,all objects fall with the same acceleration because '$g$' is independent of the mass of the falling body. The value of '$g$' is approximately $9.8 \, m/s^2$.