Question

What is the work (in $\text{J}$) put into a simple machine for an output work of $25\text{J}$, if the machine is only $55\%$ efficient?

• A. 45.45

Answer 1

The correct option is A 45.45
Given:
The output work of the machine, $\text{O.W.}=25\text{J}$
The efficiency of the machine, $\text{E}=55\%=\frac{55}{100}=0.55$
We know that the efficiency of a machine is the ratio of the output work to the input work, i.e. if $\text{I.W.}$ is the work put into the machine then,
$\text{E}=\frac{\text{O.W.}}{\text{I.W.}}$
$⟹0.55=\frac{25}{\text{I.W.}}$
$⟹\text{I.W.}=\frac{25}{0.55}=\frac{2500}{55}=\frac{500}{11}$
$⟹\text{I.W.}=45.45\text{J}$