Question

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

• A. $\left(i\right)1.25J,\left(ii\right)–8.25J$
• B. $\left(i\right)100J,\left(ii\right)8.75J$
• C. $\left(i\right)10J,\left(ii\right)–8.75J$
• D. $\left(i\right)–10J,\left(ii\right)–8.25J$

Answer 1

The correct option is C $\left(i\right)10J,\left(ii\right)–8.75J$

$m=1g=\frac{1}{1000}kg$
$h=1km=1000m$
Work done by gravitional force $W_g=mgh$
$W_g=\frac{1}{1000}\times 10\times 1000=10J$
Change in kinetic energy, $△K.E=\frac{1}{2}m{v}^2-0$
$=[\frac{1}{2}\times \frac{1}{1000}\times 50\times 50]-0$
$=1.25J$
By work energy theorem, $W_g+W_{airresistance}=△K.E$
$10+W_{airresistance}=1.25$
$\Rightarrow W_{airresistance}=-8.75J$