Question

A water pump rated 400 W, has an efficiency of 75%. If it is employed to raise water through a height of 40 m, the volume of water drawn in 10 min is :

• A. $0.45m^3$
• B. $0.75m^3$
• C. $0.62m^3$
• D. $0.02m^3$

Answer 1

The correct option is A $0.45m^3$

Output power $=\eta \times inputpower$
$=0.75\times 400=300W$
Now, from $P=\frac{dw}{dt}=\frac{d\left(mgh\right)}{dt}$
$\frac{dm}{dt}=\frac{P}{gh}=\frac{300}{10\times 40}=\frac{3}{4}kg$
$\frac{3}{4}\times 60kgmi{n}^{-1}$
$45kgmi{n}^{-1}$
Hence, water drawn in 10 min
$45\times 10=450kg$
Since, density of water $=1000kg{m}^{-3}$
Therefore, from $m=\rho V$
$V=\frac{m}{\rho }=\frac{450}{1000}=0.45m^3$