Question

A pump ejects 12000kg of water at the speed of 4m/s in 40 second. Find the average rate at which the pump is working
A. 2.4kW
B. 2.5kW
C. 2.3kW
D. 1.7kW

Answer 1

Hint:In physics, power is defined as the rate at which work is done. Or in other words it can be said that power is the amount of work done or energy converted in a unit time.

Formula Used:
Mathematically, the power is written as
\[P = \dfrac{W}{t}\]……(i)
Where ‘P’ is the power, ‘W’ is the work done and ‘t’ is the time taken to do work.

Complete step by step solution:
Given that the amount of water ejected by the pump is, m=12000 kg.
The time taken by the pump to eject water is, t=40 second.
Speed of the water pump is, v=4 m/s.
Equation (i) can be written as,
\[P = \dfrac{{F.s}}{t}\]……(ii)
In order to find out the force, use formula, $F=ma$
Substituting the values given and solving, we get
\[F = 12000 \times \dfrac{4}{{40}}\]
$\Rightarrow F=1200\,N$

The displacement can be calculated by using equation of motion, we get
\[s = ut + \dfrac{1}{2}a{t^2}\]
Initial speed is u=0
Substituting all the values in the above equation of motion we get
\[s = (0)t + \dfrac{1}{2} \times \dfrac{{(4 - 0)}}{{40}} \times {(40)^2}\]
$\Rightarrow s=80\,m$

Now we have the values of force and displacement, so substituting them in equation (ii), we get
\[P = \dfrac{{1200 \times 80}}{{40}}\]
$\Rightarrow P=2400\,Watt$
$\therefore P=2.4\,kW$
Hence, the average rate at which the pump will be working is 2.4kW.

Therefore, Option A is the correct answer.

Note: It is important to note that power is different from energy. Energy is the capacity to do work but power is the rate at which work is done or energy is transferred. Also, energy can be transferred from one form to another. On the other hand, power can not be transferred from one form to another.