Question

A pumping machine pumps a liquid at a rate of $60$ cc per minute at a pressure of $1.5$ atmosphere. Power of the machine is:
A. $9\,watts$
B. $6\, watts$
C. $9\,Kw$
D. none of these

Answer 1

We can use the standard definition of power of a machine to solve this problem. Power is the ratio of work done to time taken. Work done can be calculated at constant pressure for the given change in volume.

Formula used:
$Power = \dfrac{{work}}{{time}}$ and
$work = pressure \times \Delta volume$.

Complete step by step answer:
Given, the volume of liquid being pumped $V = 60cc = 60 \times {10^{ - 6}}{m^3}$.
The pressure of liquid being pumped $P = 1.5atm = 1.5 \times {10^5}P$
Time to perform the work t$= 1s$
Work done is defined as a product of pressure and volume, when there is a change in volume. Work done$=$pressure$\times$volume.
Substituting the values given in the question we get,
Work done $= 1.5 \times {10^5} \times 60 \times {10^{ - 6}}$
$\Rightarrow$ Work done $= 90 \times {10^{ - 1}} = 9J$
Therefore the work done by the pumping machine is 9J.
Power is defined as a rate at which the work is done.
$Power = \dfrac{{work}}{{time}}$.
Substituting the value of work and time in the above equation, we get
$Power = \dfrac{9}{1} \\\ \therefore Power = 9\,watts$
Therefore we get the power of the machine 9 watts.

Hence, option A is the correct answer.

Additional information:
Power of a machine is defined as the extent of work which the machine can perform in a particular time period. It is the rate of transfer of energy. Machine saves energy and helps to perform tasks with ease.

Note: We should know the standard definition of power that is the rate at which work is done or may be defined as the ratio of work done to the time taken. The work done should be in Joule to obtain power in watt. Wrong units may result in errors in answers to such types of questions.