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 the (ii) resistive force of airs is:

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

Answer 1

The correct option is A $\left(i\right)10J\left(ii\right)-8.75J$

$m=1g=\frac{1}{1000}kg$

$h=1km=1000m$

work done by gravitional force $w_g-mgh$
$wg=\frac{1}{1000}\times 10\times 1000$
Change in kinetic energy $△K.E=\frac{1}{2}m{v}^2-0$
$=\frac{1}{2}\frac{1}{1000}\times 50\times 50-0$
$=1.25J$
Work energy theorem: $w_g+w_{airresistance}=△K.E$
$10J+resistance=1.25-10$
where resistance$=-8.75J$