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 $50\,m/s$. Take 'g' constant with a value ${10 \, m/s^2}$. The work done by the (i) gravitational force and the (ii) resistive force of air is :-

• A. (i) 1.25 J (ii) - 8.25 J
• B. (i) 100 J (ii) 8.75 J
• C. (i) 10 J (ii) - 8.75 J
• D. (i) - 10 J (ii) - 8.25 J

Answer 1

Answer: (C)

(i) 10 J (ii) - 8.75 J

Answer 2

Sol. $w_{g}+w_{a}=K_{f}-K_{i}$
$m g h+ w_{a}=\frac{1}{2} m v^{2}-0$
$10^{-3} \times 10 \times 10^{3}+w_{a}=\frac{1}{2} \times 10^{-3} \times(50)^{2}$
$w_{a}=-8.75\, J$ i.e. work done due to air resistance and work done due to gravity $=10\, J$