Q112 / 200 · NEET 2008 (Screening) · Physics

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? $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

  • Correct answer
    A
    $8.1 \mathrm{~kW}$
  • B
    $10.2 \mathrm{~kW}$
  • C
    $12.3 \mathrm{~kW}$
  • D
    $7.0 \mathrm{~kW}$

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 $\begin{aligned} & \frac{M}{t}=15 \mathrm{~kg} / \mathrm{s}, g=10 \mathrm{~m} / \mathrm{s}^2, h=60 \mathrm{~m} \\ & P_{\text {generated }}=(15 \times 10 \times 60) \times \frac{90}{100} \\ &=8.1 \mathrm{~kW} \end{aligned}$

Hence, the correct answer is option: 'A'.

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