Question

A pump of 5HP can lift 36000 litres water in 8 hours .The correct relation is. (a)If power of pump is constant then quantity of water is inversaly proportional to time. (b)If quantity of water is constant then time is directly proportional to the power of pump. ( c)If time is constant then quantity of water inversaly proportional to power of the pump. (d)If power of the pump is constant then quantity of water is directly proportional to time​

Answer 1

so 10 is your answer

Step-by-step explanation:

I have explained all methods

please mark me as Brainalist

Answer 2

The correct relation is if the power of the pump is constant then the quantity of water is directly proportional to the time. (option d)

What is power?

• ​Power is the rate of work done.
• Its commercial unit is Kilowatt-per-hour (kWh).
• It is calculated as:

                              P = $\frac{E}{t}$

where E is the energy of the system

    and t is the time

• In the given question, the energy possessed by the lifting of water is potential energy.
• Potential energy is given by:

                                  U = mgh

where m is the mass/quantity of the water

           g is the acceleration due to gravity

      and "h" is the height to which water is raised.

• So power is given by:

                                P = $\frac{U}{t}$

                           ⇒ P = $\frac{mgh}{t}$                                         (1)

So now we analyze each option.

(a)If the power of the pump is constant then the quantity of water is inversely proportional to the time.

• If power is constant then $\frac{mgh}{t}$ will also be constant. Hence, if the quantity of water increases, then time must also increase.

                               Pt = mgh

                            ⇒ m ∝ t

• Hence, this option is wrong.

(b)If the quantity of water is constant then time is directly proportional to the power of the pump.

• If the quantity of water is constant, m in (1) will be constant.
• It is clear from (1) that power is inversely proportional to time.
• Thus, this option is wrong.

(c)If time is constant then the quantity of water is inversely proportional to the power of the pump.

• If time is constant, mgh = P.
• Thus, the quantity of water is directly proportional to the power.
• Hence, this option is wrong.

From the explanation of (a), it is clear that the correct option is (d) If the power of the pump is constant then the quantity of water is directly proportional to time​.