Question

The power of the water pump is $ 4kW $. If $ g = 10m{s^{ - 2}} $ the amount of water it can raise in $ 1 $ minute to a height of $ 20m $ is
(A) 100 litre
(B) 1000 litre
(C) 1200 litre
(D) 2000 liter

Answer 1

Hint: For water, the mass $ m $ and the volume $ V $ are equal since the density is 1 kg per litre. The SI unit of power is watt, which is one joule per second. We can find the amount of water by finding the work done by the pump which is the product of the power and time.

Formula Used: The following formulas are used to solve this question.
 $ Power = \dfrac{{{\text{Work done}}}}{{{\text{time}}}} $
 $ {\text{Work done = }}mgh $ where $ m $ is the mass, $ g $ is the acceleration due to gravity and $ h $ is the height.

Complete step by step answer
Energy can be defined as the capacity for doing work.
Work can be defined as transfer of energy. In physics we say that work is done on an object when you transfer energy to that object. Work is the application of a force over a distance.
Power is defined as the amount of energy transferred or converted per unit time. Since, work done is equivalent to the change in energy, power can also be expressed as work per unit time. The S.I. unit of power is the watt (W), equal to one joule (J) per second(s).
It is given in the question, that the power of the water pump is $ 4kW $.
 $ 1kW = 1000W $
 $ \therefore 4kW = 4000W $
Potential energy (P.E.) is the energy stored in an object and is measured by the amount of work done. Work done is thus given by-
 $ {\text{Work done}} = mgh $ where $ m $ is the mass, $ g $ is the acceleration due to gravity and $ h $ is the vertical height from a chosen reference frame.
Let mass be $ m $. Given that, is the acceleration due to gravity $ g = 10m{s^{ - 2}} $ and height $ h = 20m $.
 $ \therefore {\text{Work done = m}} \times 10 \times 20 = 200{\text{m J}} $
We know that the density of water is $ 1000kg{m^{ - 3}} = 1kg{l^{ - 1}} $, thus $ m = V $ for water, where $ m $ is mass and $ V $ is the volume.
 $ \therefore {\text{Work done = }}200{\text{m J = 200V J}} $
It is known to us that, $ Power = \dfrac{{{\text{Work done}}}}{{{\text{time}}}} $
Given that, $ Power = 4000W $ and $ \therefore {\text{Work done = }}200V{\text{ J}} $
Thus, $ 4000 = \dfrac{{200m}}{t} $ where $ t $ is the time in seconds.
To find volume in 1minute, $ t = 60s $.
 $ 4000 = \dfrac{{200V}}{{60}} $
 $ \Rightarrow \dfrac{{4000 \times 60}}{{200}} = V $
Thus the amount of water is given by-
 $ V = 1200l $

The correct answer is Option C.

Note
The output power of a motor is mechanical power and is equivalent to the product of its torque and angular velocity. The power involved in moving a ground vehicle is the product of the traction force on the wheels and the velocity of the vehicle. The rate at which a light bulb converts electrical energy into light and heat is measured in watts – the electrical energy used per unit of time. In this case, power is called electrical power.