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Question

A pump is used to lift 500kg of water from a depth of 80m in 10s. Calculate the power rating of the pump if its efficiency is 40%


A

100kW

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B

40kW

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C

16kW

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D

None of the above

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Solution

The correct option is A

100kW


Step 1: Calculate the force exerted by the pump

Given, mass of the water lifted is 500kg

We know that F=mg, where F is the force exerted, m is the mass of the object and g is the acceleration due to gravity. Assuming g=10ms-2,

F=500×10F=5000N

There the pump exerts 5000N of force.

Step 2: Calculate the work done by the pump

Given, water is moved 80m high.

The formula for calculating work done is,

W=F·s

Where, W is the work done, F is the force exerted and s is the displacement of the object.

Thus, work done is,

W=5000·80W=400000=4×105J

Therefore, the pump does 4×105J of work.

Step 3: Calculate the power of the pump

Given, the pump does the work in 10s

The formula for power (P) is given as,

P=Wt

Where, t is the time taken to do the work.

Thus,

P=4×10510=40kW

Step 4: Calculate power rating

Given, efficiency=40%=0.4

We know that,

Powerrating=Usefulpowerefficieny

Thus, the power rating of the given pump is,

Powerrating=400.4=100kW

Hence, option A is correct.


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