Question

A water pump raises 50 litres of water through a height of 25m in 5s. Calculate the power which the pump supplies. (Take $g = 10Nk{g^{ - 1}}$ and density of water $ = 1000kg{m^{ - 3}}$)
A. 2500W
B. 12.5KW
C. 2500KW
D. None of the above

Answer 1

Hint: The question talks about a pump installed below a certain height and customized or expected to pump a certain volume or amount of water with the power unknown, the force applied and the cross sectional area.

Complete step by step answer:
We are given that a water pump raises 50 litres of water through a height of 25m in 5s.
We need to solve for mass first.
Density is the ratio of mass to the volume.
$D = \dfrac{m}{V}$
Using the above formula, find the mass
$1000kg{m^{ - 3}} = \dfrac{{mass}}{{50 \times 0.001{m^3}}}$
One cubic meter is equal to 1000 litres.
The volume of water was given in litres but then we need to convert the litres to ${m^3}$. It can be done by dividing by 1000 so that our unit can be uniform and be the same. Then we cross multiply
Mass = $1000 \times 50 \times 0.001 = 50kg$
Energy generated or work done by the power is represented by the relation ${E_p} = mgh$, where ${E_p}$ is the energy produced, m is the mass, g is acceleration due to gravity and h is the height,
${E_p} = 50 \times 10 \times 25 = 12500J$
Power is the ratio of energy to time, to solve for power we will be applying the formula
$Power = Energy/Time$
Energy is 12500J and the time is 5 seconds.
Therefore, Power is equal to
$P = \dfrac{{12500}}{5} = 2500W$.

So, the correct answer is “Option A”.

Note:
When we are given a solution for a value and the units of all the remaining values are irrelevant, then we have to convert them into the same system of units. Here the volume is given in litres but density is given in cubic meters, so we have to convert either density into litres or volume into cubic meters to solve for mass. That is what we have done. One cubic meter is also equal to 1000 litres which means one litre is one thousandth of one cubic meter.