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Question

A person decided to use his bath tub water to generate electric power to run a 40W bulb. The bath tub is located at a height of h meters from ground and it holds V litres of water. He installs a water driven wheel generator on ground. The rate in m3/s at which water should drain from bath tub to light the bulb, if efficiency of machine be 90%, is (Given density of water =ρ and acceleration due to gravity =g)

A
11.11ρgh
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B
33.33ρgh
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C
44.44ρgh
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D
22.22ρgh
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Solution

The correct option is B 44.44ρgh
Power=P=dWdt=ddt(mhg)

=dVρghdt

or P=dVρghdt=pdhdVdt

Since efficiency η=PoutputPinput

Poutput=ηPinput=ηρghdVdt

or dVdtη=Poutputηρgh2

dVdt=400.9ρgh=44.44ρgh

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