Question

Two machines A and B have efficiencies in the ratio 3:4. If the work done on machine A is 1200 J and on machine B is 1800 J, then what is the ratio of the work done by A to B

Answer 1

As efficiency is given by, η= $\frac{P_{output}}{P{}_{input}}$
Work done on the machine is given as P_input and work done by the machine is calculated as P_output.
Given, $\frac{{\eta }_1}{{\eta }_2}$= $\frac{3}{4}$
P₁ input = 1200 J
and P₂ input= 1800 J
Applying above formula and solving :-
We get :- $$\begin{gathered} \frac{{\eta }_1}{{\eta }_2}=\frac{({\displaystyle \frac{P_O}{P_i}}{)}_1}{({\displaystyle \frac{P_O}{P_i}}{)}_2}=\frac{P_{o1}}{P_{o2}}X\frac{P_{i2}}{P_{i1}} \\ \frac{P_{o1}}{P_{o2}}=\frac{{\eta }_1}{{\eta }_2}\frac{P_{i1}}{P_{i2}}=\frac{3}{4}\frac{1200}{1800}=\frac{1}{2} \end{gathered}$$
Putting the values from above:
( $\frac{P_1}{P_2}$)_{output= $\frac{1}{2}$}