Question

The power of a motor pump is $2kW$. How much water per minute the pump can raise to a height of $10m$? ($g = 10m/{s^2}$)
A)$300kg$
B)$600kg$
C)$1200kg$
D)$2400kg$

Answer 1

Hint: We know that power is the energy delivered per unit time. Energy delivered is the energy required to raise the water to a height of $10m$ in this case. Energy gained by water when it rises to a certain height is in the form of gravitational potential energy.

Complete answer:
Power of the motor is given,
$P = 2kW = 2000W$
We know that power is the rate of energy delivered by the pump so it can be written as.
$P = \dfrac{E}{t}$ …... equation 1
Energy gained by water when it raises to a certain height is in the form of gravitational potential energy is written as,
$E = Mgh$
And as we know the value of $g$ is $10m/{s^2}$ according to the question and height up to which water is raised by the pump i.e., $h = 10m$. So we can write gravitational potential energy as
$E = M(10)(10)$
$\Rightarrow E = 100M$
Where $M$ is the mass of water which is raised by the pump to height $10m$
Putting the value in equation 1 we will get
$2000 = \dfrac{{100M}}{{60}}$
$\Rightarrow M = 1200kg$

Therefore, The pump can raise a mass of $1200Kg$ water to $10m$ height in one minute. So, Option (C) is correct.

Additional Information:
In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity which means that it only has magnitude and does not have any direction.

Note:
By definition, power is the amount of energy transfer in one second. Please remember that potential energy is the energy stored in the body due to its position. So whenever a body is raised to some height, it means we are doing work against gravity and that work will be stored in the form of gravitational potential energy.