Question

The Power of a motor which is raising 200kg of water in ten minutes from a well of depth 60m is ......

Given Answer is 196w .....prove it

Answer 1

SoluTion :-

✴ Given :-

• Mass of water = 200kg
• Time interval = 10min
• Depth of well = 60m

✒ 10 min = 600 s

✴ To Find :-

• Power of motor

✴ Concept :-

✈ Power is defined as ratio of work done to the time and as per work-energy theorem work done is always equals to the change in energy.

✴ Calculation :-

$\implies\sf\:Power=\dfrac{Work\:done}{Time}=\dfrac{\triangle{PE}}{Time}\\ \\ \implies\sf\:P=\dfrac{mgH}{t}\\ \\ \implies\sf\:P=\dfrac{200\times 9.8\times 60}{600}\\ \\ \implies\sf\:P=\dfrac{1960}{10}\\ \\ \implies\:\boxed{\tt{\large{\orange{Power=196\:Watt}}}}$

✴ Additional information :

• Work, energy and power all are scalar quantities.
• Scalar quantity has only magnitude.
• Power is also defined as rate of work done.

Answer 2

GiveN :

• Mass of motor (m) = 200 kg
• Depth of well (h) = 60 m
• Time (t) = 10m = 600 s

To FinD :

• Power required by motor

SolutioN :

Use formula for Power :

$\dashrightarrow \boxed{\tt{P \: = \: \dfrac{Work}{Time}}} \\ \\ \dashrightarrow \tt{P \: = \: \dfrac{mgh}{t}} \\ \\ \dashrightarrow \tt{P \: = \: \dfrac{200 \: \times \: 9.8 \: \times \: 60}{600}} \\ \\ \dashrightarrow \tt{P \: = \: \dfrac{12000 \: \times \: 9.8}{600}} \\ \\ \dashrightarrow \tt{P \: = \: 20 \: \times \: 9.8} \\ \\ \dashrightarrow \tt{P \: = \: 196} \\ \\ \underline{\sf{\therefore \: Power \: required \: by \: motor \: is \: 196 \: W}}$

_______________________

Additional information :

• SI unit of power is Watt (W)

• Power is defined as Rate of doing Work.

• Denoted by P.

• It is scalar quantity.