Question

A water pump raises 50 liters of water through a height of 25m in 5 sec. Calculate the power of the pump required. [g = 10Nkg-1, density of water 1gm cm-3]

Answer 1

$\huge \rm {Answer:-}$

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$\sf \red {\underline{Given:}}$

$\mapsto \tt {Volume\: of\: water\: raised=50\: litres}$

★Converting it into cubic metres

$\colon \implies \tt {50\times10^{-3}m^{3}}$

$\mapsto \tt {Height\: of\: water\: raised=25\: metres}$

$\mapsto \tt {Time(t)=5\: seconds}$

$\mapsto \tt {Density=1gmcm^{3}}$

★Converting C.G.S to M.K.S

$\colon \implies \tt {1000kgm^{3}}$

$\mapsto \tt {g=10Nkg^{-1}}$

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$\sf \blue {\underline{To\: find:}}$

★Power that the pump required=?

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★To find power,we need to know the work done,to know the work done,we need to now mass. so the basic formula for the calculation of power would be :-

$\mapsto \tt {\fbox{Mass=Volume×Density}}$

$\colon \implies \tt {50\times10^{-3}m^{3}\times 1000kgm^{3}}$

$\colon \implies \tt {50\times{\cancel{10^{-3}m^{3}}}\times {\cancel{1000}}kg{\cancel{m^{3}}}}$

$\mapsto \tt \pink{\fbox{Mass=50kg}}$

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★As the mass is determined,we can find the work done.

$\mapsto \tt {\fbox{Work\: done(W)=mgh}}$

★where,

★m= mass,g= acceleration due to gravity and h=height

$\colon \implies \tt {W=50kg\times10Nkg^{-1}\times25m}$

$\colon \implies \tt {W=50{\cancel{kg}}\times10N{\cancel{kg^{-1}}}\times25m}$

$\colon \implies \tt {W=50\times10N\times25m}$

$\colon \implies \tt {W=12,500Nm}$

$\mapsto \tt \purple{\fbox{Work\: done=12500\: Joules}}$

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★As the work done is determined too,we can finally find out the power !

$\large \mapsto \tt {Power=\frac{work\: done}{Time\: taken}}$

$\large \colon \implies \tt {power=\frac{12500J}{5s}}$

$\large \colon \implies \tt {power=\frac{\cancel{12500}J^{2500}}{\cancel{5}s}}$

$\colon \implies \tt {power=2500Js^{-1}}$

$\mapsto \tt \green{\fbox{Power=2500Watts}}$

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$\sf \orange {\underline{Henceforth,:}}$

★The power that the pump required is 2500 watts

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