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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/s². The work done by the (i) gravitational force and the (ii) resistive force of air is:

1. (i) 1.25 J (ii) −8.25 J
2. (i) 100 J (ii) 8.75 J
3. (i) 10 J (ii) −8.75 J
4. (i) −10 J (ii) −8.25 J

Correct answer: (i) 10 J (ii) −8.75 J

Solution

The work done by the gravitational force is mgh = (0.001 kg)(10 m/s²)(1000 m) = 10 J. The kinetic energy at impact is (1/2)mv² = (1/2)(0.001 kg)(50 m/s)² = 1.25 J. The resistive force does negative work, equal to the difference between the gravitational work and the final kinetic energy: −(10 J − 1.25 J) = −8.75 J.

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