Question
How much water a pump of $$2\,kW$$ can raise in one minute to a height of $$10\,m$$ ?
(Take $$g = 10\,m/{s^2}$$ )
A.
$$1000\,L$$
B.
$$1200\,L$$
C.
$$100\,L$$
D.
$$2000\,L$$
Answer :
$$1200\,L$$
Solution :
Power of a body is defined as the rate at which the body can do the work, i.e.
$${\text{Power}} = \frac{{{\text{work}}}}{{{\text{time}}}} = \frac{W}{t}$$
Given, power, $$P = 2\,kW = 2000\,W$$
$$\eqalign{
& W = Mgh = M \times 10 \times 10\,\,\left[ {\because g = 10\,m/{s^2}} \right] \cr
& = 100\,M \cr} $$
Time, $$t = 60\,s$$
$$\eqalign{
& \therefore 2000 = \frac{{100M}}{{60}} \cr
& \therefore M = 1200\,kg \cr
& {\text{and}}\,V = 1200\,L \cr} $$