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Question

Consider a rain drop of mass 1 g falling from a height of 2 km. It hits the ground with a speed of 50 m/s. The work done by resistive force of air is
(g=10 m/s2)

A
187.5 J
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B
43.75 J
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C
18.75 J
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D
14.375 J
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Solution

The correct option is C 18.75 J
We know that by the work energy theorem, net work done = Change in kinetic energy

The sum of the workdone by gravity and work done by the resistive force in air will be equal to the change in the kinetic energy of a rain drop.

The initial velocity, v1=0 as it is dropped and let the final velocity be v2=50 m/s as given in the problem and the mass is given as m=1 g=11000 kg

We know, Wgravity=mgh, Change in kinetic energy =12m(v22v21)
Wgravity+Wresistive force=12m(v22v21)

mgh+Wresistive force=12m(v2202)

(11000)×10×2000+Wresistive force=12×11000(502)

Wresistive force=1.2520

The work done by the resistive force is =18.75 J

Hence option C is the correct answer

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