Question

A pump delivers water at the rate of 2400
litres in six minutes over a head of 12
m. If g = 10 m/s?, its power is
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Answer 1

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✤ Required Answer:

✒ GiveN:

• Amount of water delivered = 2400 l
• Time taken = 6 minutes
• Height upto which it is raised = 12 m
• [g considered = 10 m/s²]

✒ To FinD:

• Power of the pump....?

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✤ How to solve?

First of all, let's understand work done by an object in raising any object upto a certain height h.

• Let us consider an object of mass m, which is raised through a height h from the ground. A force equal to the weight( =mg) of the object is required to this. The object gains energy = work done on it$.$

⭐ Ep = W = mgh

Power - Power is the rate of work is done.

⭐ P = W/t

So, After finding the work, we are provided with time taken of doing the work. We can simply divide work by time, and find out the power of the pump?

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✤ Solution:

We have,

• g = 10 m/s²
• h = 12 m

It is approximated that, 1 litre of any substance like water, nearly weighs 1 kg. So, Here 2400 l = 2400 kg(approx.)

• m = 2400 kg
• And, t = 6 × 60 s

Finding the work done by using formula,

➝ W = mgh

➝ W = 2400 × 10 × 12 Joules

➝ W = 288000 Joules

Now, finding the power,

➝ P = W/t

➝ P = 288000/6×60 Watt

➝ P = 288000/360 Watt

➝ P = 800 W

✒ Therefore, Power of the pump = 800 W

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