Question

Calculate the power of a pump which can lift 100 kg of water to store it in a water tank at a height of 19 m in 25 s? (Take the value of g = 10 m/s².)

Answer 1

Step 1: Given data

Mass of water is, $m=100kg$

Height of water tank is, $h=19m$

Time taken to lift the water is, $t=25s$

Acceleration due to gravity is taken as, $g=10m/s^2$

Step 2: Calculating work done

Work done is given as,

$W=mgh$

where, $m$ is mass, $g$ is acceleration due to gravity and $h$ is height.

Substituting the given values in the equation for work done, we get

$$\begin{gathered} W=100kg\times 10m/s^2\times 19m \\ W=19000J \end{gathered}$$

Step 3: Calculating power

Power is given as,

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

where, $W$ is work done and $t$ is time.

Substituting the known values in the equation for power, we get,

$$\begin{gathered} P=\frac{19000J}{25s} \\ P=760W \end{gathered}$$

Therefore, the power of the pump is $760W$.