Waterfalls from a height of $60 m$ at a rate of $15 k g / s$ to operate a turbine. The losses due to frictional forces are $10$ % of energy. How much power is generated by the turbine?
$(g = 10 m / s^{2})$

12.3 k W

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7.0 k W

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8.1 k W

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10.2 k W

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Solution

The correct option is D $8.1 k W$
Energy used per $s e c^{- 1}$ to operate turbine
$= m g h = 151060$ joule
$= 9000$ joule
Power supplied to turbine $= 9000 j o u l e s e c^{- 1}$
Power loss due to friction $= 900 j o u l e s e c^{- 1}$
Power generated by turbine
$= (9000 - 900) j o u l e s e c^{- 1}$
$= 8100 j o u l e s e c^{- 1} = 8.1 k W$

Second approach

$P_{g e n e r a t e d} = P_{i n p u t} \times \frac{90}{100} = \frac{m g h}{t} \times \frac{90}{100}$

$= \frac{15 \times 10 \times 60 \times 90}{100} = 8.1 k W$

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