Question

A pump of 200W power is lifting 2kg water from an average depth of 10m in one second. Velocity of water delivered by the pump is
(A) 10m/s
(B) 2m/s
(C) 4m/s
(D) 1m/s

Answer 1

Hint: This is a straight question where the formula of power can be used. After that use the explicit formula of energy. As we know that power is equal to energy per unit time. Since height is mentioned in the question, therefore, put the value of energy as mgh. Just used the formula and given data in the question. Put the value in the formula and get the answer.

Complete step by step answer
Power is defined as energy per unit time.
Mathematically.
$power = \dfrac{{energy}}{{time}}$
$power = \dfrac{{mgh}}{t}$
Acceleration due to gravity is equal to$\left( {\mathop {g = 10m/s}\nolimits^2 } \right)$
Height(H)$ = 10metres$
Mass=2kg
We know that the potential energy= mgh
$ \Rightarrow 2 \times 10 \times 10 = 200J$
As, $power = \dfrac{{energy}}{{time}}$
When power of motor=200W
$200 = \dfrac{{200}}{t}$
$ \Rightarrow t = 1\sec $
Here the displacement of water=height=10m
Time= 1sec
Hence, $velocityV = \dfrac{{Displacement}}{{Time}}$
So, $V = \dfrac{{10}}{1} = 10m/\sec $
So, the velocity of water delivered by the pump is 10m/s.

So, our correct answer is option A.

Additional information

$1Watt = 1J/s$
One minute=60 second
Velocity of acceleration due to gravity$(g) = \mathop {9.8m/s}\nolimits^2 $
1K=1000gram(g)
Density of water= 1000kg/cubic-meter
If you want to convert it into litres then,
$volume = \dfrac{{mass}}{{density}}$

Note: Using the formula of energy which is defined as the product of acceleration due to gravity, mass and height. Assume acceleration due to gravity (g) as 10 which is an approximation of 9.8 to make calculation easy. Generally, when the body is in motion, we use kinetic energy and when the body is at the same height then we use potential energy. In this question we use potential energy which can be written as only energy. Note that the body is the same height.