A pump is used to lift of water from a depth of in . Calculate the power rating of the pump if its efficiency is
Step 1: Calculate the force exerted by the pump
Given, mass of the water lifted is
We know that , where is the force exerted, is the mass of the object and is the acceleration due to gravity. Assuming ,
There the pump exerts of force.
Step 2: Calculate the work done by the pump
Given, water is moved high.
The formula for calculating work done is,
Where, is the work done, is the force exerted and is the displacement of the object.
Thus, work done is,
Therefore, the pump does of work.
Step 3: Calculate the power of the pump
Given, the pump does the work in
The formula for power () is given as,
Where, is the time taken to do the work.
Step 4: Calculate power rating
We know that,
Thus, the power rating of the given pump is,
Hence, option A is correct.