Question

In how much time can a water pump 500w lift 1000 kg of an overhead tank situated at a height of 7 metre??

Answer 1

Given :

▪ Power of water pump = 500W

▪ Mass of tank = 1000kg

▪ Height = 7m

To Find :.

▪ Time taken by pump to lift the tank.

Concept :

✒ Power is defined as the rate of work done per unit time.

✒ Power is a scalar quantity.

✒ It has only magnitude.

Mathematically,

$\bigstar\:\underline{\boxed{\bf{\pink{Power=\dfrac{Work\:done}{Time}}}}}$

Calculation :

$:\implies\sf\:P=\dfrac{W}{t}\\ \\ :\implies\sf\:P=\dfrac{F\times d}{t}\\ \\ :\implies\sf\:P=\dfrac{(mg)\times d}{t}\\ \\ :\implies\sf\:t=\dfrac{(mg)\times d}{P}\\ \\ :\implies\sf\:t=\dfrac{1000\times 10\times 7}{500}\\ \\ :\implies\sf\:t=2\times 70\\ \\ :\implies\underline{\boxed{\bf{\green{t=140s=2min\:20s}}}}\:\orange{\bigstar}$

Answer 2

$\huge\sf\red{Answer:}$

☆ According to the question:

⇒ Let's find the time taken by a water pump 500w lift 1000 kg of an overhead tank situated at a height of 7 metre.

☆ Using formulas:

☆ ${\sf{\underline{\boxed{\green{\sf{Power = \dfrac{Work \: Done}{Time}}}}}}}$

☆ ${\sf{\underline{\boxed{\green{\sf{Power = \dfrac{Force}{Displacement}}}}}}}$

☆ ${\sf{\underline{\boxed{\green{\sf{Power = \dfrac{Mass \times Acceleration \: gravity}{Displacement}}}}}}}$

☆ ${\sf{\underline{\boxed{\green{\sf{Time = \dfrac{Mass \times Acceleration \: gravity}{Power}}}}}}}$

☆ Calculations:

⇒ $\sf Time = \dfrac{100 \times 10 \times 7}{500}$

⇒ $\sf Time = 2 \times 70 = 140$

⇒ ${\sf{\underline{\boxed{\green{\sf{ 140 \: seconds}}}}}}$

Therefore, 140 seconds is the time taken.