Question

How much water a pump of $2kW$ can raise in one minute to a height of $10m$. Take $g=10m/s^2$?

Answer 1

Step 1: Given

Power $P=2kW=2000W$

Time taken $t=1min=60s$

Height $h=10m$

Acceleration due to gravity $g=10m/s^2$

Step 2: Derive the formula

We know that power is defined as the rate of doing work, If $W$ is the work done,

$P=\frac{W}{t}$ $\left(1\right)$

Also, $W=Fh$

Where $F$ is the force and $h$ is the height.

Therefore, $F=mg$

Where $m$ is the mass and $g$ is the acceleration due to gravity.

Substituting these in equation $\left(1\right)$ we get,

$P=\frac{mgh}{t}$

$\Rightarrow m=\frac{Pt}{gh}$ $\left(2\right)$

Step 3: Calculate the mass

Upon substituting the values in equation $\left(2\right)$ we get,

$m=\frac{2000\times 60}{10\times 10}$

$=1200kg$

Hence, the pump can lift $1200kg$ of water.