Question

The power of a pump motor is 2 kw. How much water per minute can it raise to a height of 10 m? (g-10 m/s) [1200 kg)

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Power of Pump (P) = 2KW = 2000 Watts.
• Height (H) = 10 meters.
• Acceleration due to gravity (g) = 10 m/s².
• Time (t) = 1 minute = 60 seconds.

$\huge{\bold{\underline{Explanation:-}}}$

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Firstly Finding the Work done.

Work Done:-

It is defined as The scalar Product of Force and Displacement.

From the Formula,

$\large{\boxed{\tt W = F.s}}$

But

• F = mg = Weight of the body.
• s = h = Height raised.

Therefore,

$\large{\tt \leadsto W = mg \times h}$

$\large{\tt \leadsto W = mgh}$

Substituting the values,

$\large{\tt \leadsto W = m \times 10 \times 10}$

$\large{\tt \leadsto W = m \times 100}$

$\large{\tt \leadsto W = 100m \: -----(1)}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Now,applying Power Concepts,

Power:-

Power is defined as rate of doing work.

It can be expressed as,

$\large{\boxed{\tt P = \dfrac{W}{t}}}$

Substituting the values,

$\large{\tt \leadsto2000 = \dfrac{100m}{60}}$

$\large{\tt \leadsto 2000 \times 60 = 100m}$

$\large{\tt \leadsto 120000 = 100m}$

$\large{\tt \leadsto m = \dfrac{120000}{100}}$

$\large{\tt \leadsto m = \cancel{\dfrac{120000}{100}}}$

$\huge{\boxed{\boxed{\tt m = 1200 \: Kg}}}$

So, the water raised per minute is 12 Kilograms.

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Answer 2

Power=Work/Time

     P=Weight/t ime

     P=mgh/t ime

   2000=m×10×10/60

   hence

    m=20×60=1200 kg=1200 L