Question

An electric pump is used to fill an overhead tank of capacity $ 9\,{{m}^{3}} $ kept at a height of $ 10\, m $ above the ground. If the pump takes $ 5 \,min $ to fill the tank by consuming $ 10 \,kW $ power the efficiency of the pump should be (Take $ g=10\text{ }m{{s}^{-2}} $ )

• A. 60%
• B. 40%
• C. 20%
• D. 30%
• E. 50%

Answer 1

Answer: (D)

Work done in raising water $ =mgh $
or $ W=(volume\times density)gh $
$ =(9\times 1000)\times 10\times 10 $
or $ W=9\times {{10}^{5}}J $
$ \therefore $ Useful power $ =\frac{work}{t} $
$ =\frac{9\times {{10}^{5}}}{5\times 60}=3\,kW $
Hence, efficiency
$ =\frac{useful\text{ }power}{consuming\text{ }power} $
$ =\frac{3}{10}=30% $