Question

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

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

Answer 1

Answer: (A)

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