Question

A pump can lift 100L of water to a height 20m in 9.8second. what is the power of the pump? ​

Answer 1

Answer:

Given:

Volume of water pumped = 100 L

Height = 20 m

Time taken = 9.8 seconds

To find:

Power of the Pump

Concept:

Power is defined as the rate of doing work. In other words , it's the ratio of work done to time taken to do the work.

Here the pump does work against gravitational force. And it's equal to the potential energy gained by the water volume.

Calculation:

Conversion of volume into mass :

100 L of water has mass 1 × 100 kg = 100 kg

$work \: = m \times g \times h$

$= > work \: = 100 \times 9.8 \times 20$

$= > work \: =( 2000 \times 9.8) \: joule$

Power can be calculated as follows :

$power \: = \dfrac{work}{time}$

$= > power \: = \dfrac{(2000 \times 9.8)}{9.8}$

$= > power = 2000 \: watt$

So final answer :

$\boxed{ \red{ \huge{ \bold{power = 2000 \: watt}}}}$

Answer 2

GiveN :

• Volume of water = 100 l
• Height upto which pump can lift = 2
• Time (t) = 9.8 s

To FinD :

• Power of pump

SolutioN :

✯ 100 L of water have equivalent weight to 100 kg water

$\bigstar{\underline{\sf{Formula \: for \: work \: done \: is \: :}}} \\ \\ \dashrightarrow \boxed{\tt{Work \: = \: mgh}} \\ \\ \dashrightarrow \tt{Work \: = \: 100 \: \times \: 9.8 \: \times \: 20} \\ \\ \dashrightarrow \tt{Work \: = \: 2000 \: \times \: 9.8} \\ \\ \dashrightarrow \tt{Work \: = \: 19600} \\ \\ \implies {\boxed{\boxed{\textsf{\textbf{Work \: Done \: = \: 19600 \: J}}}}}$

$\rule{200}{2}$

$\bigstar{\underline{\sf{Formula \: for \: Power \: is \: :}}} \\ \\ \dashrightarrow \boxed{\tt{Power \: = \: \dfrac{Work \: Done}{Time}}} \\ \\ \dashrightarrow \tt{Power \: = \: \dfrac{19600}{9.8}} \\ \\ \dashrightarrow \tt{Power \: = \: 2000} \\ \\ \implies {\boxed{\boxed{\textsf{\textbf{Power \: consumed \: is \: 2000 \: W}}}}}$