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Question

Water falls down a 500.0 m shaft to reach a turbine which generates electricity. How much water must fall per second in order to generate 1.00×109 watts of power?(Assume 50% efficiency of conversion and g=10m/s2)

A
250m3
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B
400m3
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C
500m3
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D
200m3
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Solution

The correct option is B 400m3
Let m be the mass of water required per second.
Power generated by water just before striking the turbine P=mgh=5000m Watts
Power transferred to the turbine Pt=0.5×P=2500m Watts
Now,
Pt=Power to be generated
2500m=109
m=4×105kg
vollume=mass/density=400m3. [Densityofwater=103kg/m3]

Hence correct answer is option B

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