Consider a drop of rain water having mass 1 g falling from a height of 1 km . It hits the ground wit

Question

Consider a drop of rain water having mass 1 g falling from a height of 1 km . It hits the ground with a speed of $50 \mathrm{~m} \mathrm{~s}^{-1}$. Take $g$ constant with a value $10 \mathrm{~m} \mathrm{~s}^{-2}$. The work done by the (i) gravitational force and the (ii) resistive force of air is\

Professor PC Thomas Classes · Answer

(c) : Here, $m=1 \mathrm{~g}=10^{-3} \mathrm{~kg}$,\ $h=1 \mathrm{~km}=1000 \mathrm{~m}, v=50 \mathrm{~m} \mathrm{~s}^{-1}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$.\ (i) The work done by the gravitational force $$ =m g h=10^{-3} 	imes 10 	imes 1000=10 \mathrm{~J} $$ (ii) The total work done by gravitational force and the resistive force of air is equal to change in kinetic energy of rain drop. $$ \begin{aligned} 	herefore \quad & W_{g}+W_{r} \end{aligned}=\frac{1}{2} m v^{2}-0 . ~\left(10+W_{r}=\frac{1}{2} 	imes 10^{-3} 	imes 50 	imes 50ight. $$ or $W_{r}=-8.75 \mathrm{~J}$\