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Question

Consider a drop of rain water having mass $$1 g$$ falling from a height of $$1km$$. It hits the ground with a speed of $$50m/s$$. Take '$$g$$' constant with a value $$10m/s^2$$. The work done by the (i) gravitational force the (ii) resistive force of airs is:


A
(i)10J(ii)8.75J
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B
(i)10J(ii)8.75J
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C
(i)1.25J(ii)8.75J
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D
(i)100J(ii)8.75J
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Solution

The correct option is A $$(i) 10J\quad (ii) -8.75J$$
$$m=1g=\dfrac{1}{1000}kg$$
 $$h=1km=1000m$$
work done by gravitional force $$w_g-mgh$$
$$wg = \dfrac{1}{1000}\times 10\times 1000$$
Change in kinetic energy $$\triangle K.E = \dfrac{1}{2}mv^2-0$$
$$=\dfrac{1}{2}\dfrac{1}{1000}\times 50 \times 50-0$$
$$=1.25J$$
Work energy theorem: $$w_g+w_{air\, resistance} =\triangle K.E$$
$$10J + resistance = 1.25-10$$
where resistance$$ = -8.75J$$    

Physics

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