Water falls from a height of $60 \mathrm{~m}$ at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a…

Water falls from a height of $60 \mathrm{~m}$ at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a turbine. The losses due to frictional forces are $10 \%$ of energy. How much power is generated by the turbine? $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$
  1. $8.1 \mathrm{~kW}$
  2. $10.2 \mathrm{~kW}$
  3. $12.3 \mathrm{~kW}$
  4. $7.0 \mathrm{~kW}$

Solution

Power generated by the turbine is,
$\begin{aligned}
P_{\text {gene rated }} & =P_{\text {input }} \times \frac{90}{100} \\
& =\frac{M g h}{t} \times \frac{90}{100}
\end{aligned}$
Putting the given values
$\begin{aligned}
& \frac{M}{t}=15 \mathrm{~kg} / \mathrm{s}, g=10 \mathrm{~m} / \mathrm{s}^2, h=60 \mathrm{~m} \\
& P_{\text {generated }}=(15 \times 10 \times 60) \times \frac{90}{100} \\
&=8.1 \mathrm{~kW}
\end{aligned}$

Asked in: NEET 2008 (Screening)

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