An engine pumps up $100 kg $ of water through a height of $10 m$ in $ 5 s. $ Given that the efficiency of the engine is $ 60\%$ . If $g = 10m{s^{ - 2}}$, the power of the engine is .............. $\mathrm{kW}$
An engine pumps up $100 kg $ of water through a height of $10 m$ in $ 5 s. $ Given that the efficiency of the engine is $ 60\%$ . If $g = 10m{s^{ - 2}}$, the power of the engine is .............. $\mathrm{kW}$
$3.3$
$0.33$
$0.033$
$33$
An engine pumps up $100 kg $ of water through a height of $10 m$ in $ 5 s. $ Given that the efficiency of the engine is $ 60\%$ . If $g = 10m{s^{ - 2}}$, the power of the engine is .............. $\mathrm{kW}$
Work output of engine $= mgh = $ $100 \times 10 \times 10 = {10^4}J$
Efficiency ($\eta$) = $\frac{{{\rm{output}}}}{{{\rm{input}}}}$
Input energy = $\frac{{{\rm{outupt}}}}{\eta }$
$ = \frac{{{{10}^4}}}{{60}} \times 100 = \frac{{{{10}^5}}}{6}J$
Power = $\frac{{{\rm{input energy}}}}{{{\rm{time}}}}$= $\frac{{{{10}^5}/6}}{5} = \frac{{{{10}^5}}}{{30}} = 3.3\;kW$
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