Question

An engine pump up 200 kg of water through a height
of 20 min 10 second. If the efficiency of the engine
is 80%. Calculate the power of the engine.
(1) 3800 W
(2) 5000 W
(3) 4900 W
(4) 4800 W​

Answer 1

$\Large\underline{\underline{\bf \red{Correct\: Question}:}}$

An engine pump up 200 kg of water through a height of 20 m for 10 second. If the efficiency of the engine is 80%. Calculate the power of the engine.

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

• Mass of water (m) = 200kg

• Height (h) = 20m

• Time (t) = 10 s

• Efficiency = 80%

$\Large\underline{\underline{\sf To\:Find:}}$

• Power of engine

$\Large\underline{\underline{\sf Formula\:Used:}}$

$\large{\boxed{\boxed{\sf \pink{Work=PE=mgh}}}}$

$\large{\boxed{\boxed{\sf \pink{Power=\dfrac{Work}{Time}}}}}$

$\large{\boxed{\boxed{\sf \pink{Total\:Power=\dfrac{Power}{Efficiency}}}}}$

$\Large\underline{\underline{\sf Solution:}}$

$\Large{\sf W=PE=mgh}$

$\implies{\sf 200×10×20 }$

$\implies{\sf 4×10^4\:J}$

$\Large{\sf Power=\dfrac{Work}{Time}}$

$\implies{\sf \dfrac{4×10^4}{10} }$

$\implies{\sf 4×10^3\:Watt}$

$\Large{\sf Total\:Power=\dfrac{Power}{Efficiency}}$

$\implies{\sf \dfrac{4×10^3×100}{80} }$

$\implies{\sf 5×10^3\:}$

$\implies{\sf \red{Total\:Power(P)=5000\:W}}$

$\Large\underline{\underline{\sf Answer:}}$

Option (b) 5000 W

⛬ Power of the engine is 5000 W