Question

A motor pump-set of efficiency $80\%$ lifts $6000$ litres of water per minute from a well $20$ meters deep. If $g=10m{s}^{-2}$, then its input power is

• A. $20kW$
• B. $25kW$
• C. $16kW$
• D. $250kW$

Answer 1

The correct option is B $25kW$

Power of motor pump with efficiency of $80\%$ is given by:
$80\%P=\frac{mgh}{t}$
$0.8P=\frac{mgh}{t}$
Where,
$m=$ mass of water pumped
$h=$ height
$t=$ time required to pump

Here,
$m=\rho \times V$
$m=1000kg/m^3\times 6000\times {10}^{-3}{m}^3$
$m=6000kg$

$\therefore P=\frac{mgh}{t}\times \frac{1}{0.8}=\frac{6000\times 10\times 20}{60\times .8}$

$P=25kW$