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 . Take constant with a value 10 . The work done by the (i) gravitational force and the (ii) resistive force of air is [2017]

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Solution

Q.
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 ${ms}^{- 1}$ . Take $g$ constant with a value 10 ${ms}^{- 2}$ . The work done by the (i) gravitational force and the (ii) resistive force of air is [2017]

1 (i) 1.25 J (ii) - 8.25 J

2 (i) 100 J (ii) 8.75 J

3 (i) 10J (ii) - 8.75 J

4 (i) - 10J (ii) - 8.25 J

Ans.
(3)

Here, $m = 1$ $g = 10^{- 3}$ $kg,$

$h = 1 km = 1000 m, v = 50 {m s}^{- 1}, g = 10 {m s}^{- 2}$

(i) The work done by the gravitational force

$= m g h = 10^{- 3} \times 10 \times 1000 = 10 J$

(ii) The total work done by gravitational force and the resistive force of air is equal to change in kinetic energy of rain drop.

$∴$ $W_{g} + W_{r} = \frac{1}{2} m v^{2} - 0$

$10 + W_{r} = \frac{1}{2} \times 10^{- 3} \times 50 \times 50$ or $W_{r} = - 8.75 J$

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