Question

An electric motor is used to fill an overhead tank of capacity $10\, m ^{3}$ kept at a height of $20 \,m$ above the ground. If the pump takes $6$ minutes to fill the tank by consuming $20 \,kW$ power the efficiency of the pump should be $\left(g=10 \,m / s^{2}\right)$

• A. $27.5 \%$
• B. $30 \%$
• C. $32 \% $
• D. $ 40 \%$

Answer 1

Answer: (A)

work done in raising water $= mgh$.
$w =($ volume $\times$ density $) \times gh \,\,\,\left(\rho=1000 kg / m ^{3}\right)$
$w =10 \times 1000 \times 10 \times 20=2 \times 10^{6} J$
Power $=\frac{\text { work }}{\text { time }}=\frac{2 \times 10^{6}}{6 \times 60}=0.0055 \times 10^{6}=5.5 \times 10^{3} $
$ P =5.5 KW $
$. \therefore $ Efficiency $=\frac{5.5}{20} \times 100=27.5 \% $