Water falls from a height of 60 , ~m at the rate of 15 ,~kg / s t… - Vidyadip

MCQ

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 force are $10\, \%$ of the input energy. How much power is generated by the turbine? $\left(g=10\, \mathrm{~m} / \mathrm{s}^{2}\right)$ (In $\mathrm{~kW}$)

A
$10.2$
✓
$8.1$
C
$12.3$
D
$7.0$

✓

Answer

Correct option: B.

$8.1$

b
$\mathrm{E}=\mathrm{mgh}$

$\mathrm{P}_{\text {input }}=\frac{\mathrm{mgh}}{\mathrm{t}}$

$=\frac{15 \times 10 \times 60}{1}=9000=9\, \mathrm{~kW}$

$10 \,\% \operatorname{loss}=0.9 \times 10^{3}$

$\mathrm{P}_{\text {output }}=9 \times 10^{3}-0.9 \times 10^{3}=8.1 \,\mathrm{~kW}$

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