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Q.

Consider a drop of rain water having mass 1g falling from a height of 1 km. It hits the ground with a speed of 50m/s. Take ‘g’ constant with a value 10 m/s². The work by the (i) gravitational force and the (ii) resistive force of air is

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a

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

b

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

c

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

d

(i) 100J; (ii) 8.75J

answer is A.

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Detailed Solution

$\begin{array}{l} W_{g} = mgh = 0 .001 \times (1 \times 10^{3}) \times 10 = 10 J \\ W_{R} = mgh - \frac{1}{2} {mv}^{2} = 10 - \frac{1}{2} \times 10^{- 3} \times 50 \times 50 \\ = 10 - \frac{2 .5}{2} = 8 .75 J \end{array}$
work done by friction is negative.

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Consider a drop of rain water having mass 1g falling from a height of 1 km. It hits the ground with a speed of 50m/s. Take ‘g’ constant with a value 10 m/s2. The work by the (i) gravitational force and the (ii) resistive force of air is