Question

If an ideal pump pumps 200 kg of water to a height of 100 m in 10 s, then the power of pump will be
A) $4 \times {10^3}W$
B) $10 \times {10^3}W$
C) $20 \times {10^3}W$
D) none of these

Answer 1

Hint
In this question, we have to find out the power of the pump and we know that power is the work done per unit time i.e. $power = \dfrac{{work}}{{time}}$, as work is in the form of energy and pump pumps the water at height so this will contain the potential energy i.e. $W = mgh$, on substituting the values, we get the desired result.

Complete step by step answer
In this question, it is given that
Mass of water is $m = 200kg$
Height at which pump will pumps the water is $h = 100m$
Time required to pump the water is $T = 10s$
In order to calculate the value of power of the pump, we know that power is simply define as the work done per unit time i.e. $power = \dfrac{{work}}{{time}}$ …………………. (1)
Now, as the pump pumps the water at the height of 100m, and we also know that work is the form of energy so the work done will be equal to the potential energy.
Potential energy at the height h is $E = mgh$
Therefore, we can write the work done as $W = mgh$ ………… (2)
Where, m is the mass and g is acceleration due to gravity is $g = 10m{s^{ - 2}}$ and h is the height
Substitute the value of mass and height from the question in equation (2), we get
$\Rightarrow W = 200 \times 10 \times 100$
$\Rightarrow W = 200000J$
Now put the value of work done and time in the equation (2), we get
$\Rightarrow power = \dfrac{{200000}}{{10}}$
$\Rightarrow power = 20000W$
$\Rightarrow power = 20 \times {10^3}W$
Hence, option (C) is correct.

Note
Here, we should remember that, generally when the body is in motion, we use kinetic energy and when the body is at some height, we use potential energy. In this question there is potential energy which can be written as only energy. Notice that the water is accumulated at some height.
Here, for making the calculations easier we use $g = 10m{s^{ - 2}}$, otherwise the exact value of gravity is $g = 9.8m{s^{ - 2}}$.