Question

The law of a lifting machine is $P = \dfrac{W}{{50}} + 1.5$ . The velocity ratio of the machine is $100$ . Find the maximum possible mechanical advantage and maximum possible efficiency of the machine
$\left( A \right)50and50\% \\\ (B)50and60\% \\\ (C)60and60\% \\\ (D)60and50\% \\\$

Answer 1

Hint : In order to solve the question, we use the velocity ratio to obtain the maximum efficiency by dividing the velocity ratio and the maximum advantage .
We can obtain the maximum advantage by slope of the given law of the machine. Then percentage calculation can be done by percentage calculation.
$\eta _{\max} = \dfrac{{m.A}}{{V.R}} \times 100\%$ For the maximum efficiency of the machine and $y = mx + c$ for the slope of the machine.

Complete Step By Step Answer:
Given,
We have the law of the lifting machine, $P = \dfrac{W}{{50}} + 1.5$
Now to find the maximum advantage of the machine we have to see the slope of the equation
So let, the slope of the machine equation is $m$ .
So slope, $m = \dfrac{1}{{50}}$
W.A here is the inverse of the slope obtained so maximum advantage here for the machine is $\dfrac{1}{m} = 50$ .
Now to find the efficiency of the machine let $\eta$ be the efficiency and $\eta$ max be the maximum efficiency of the machine.
So according to the efficiency, $\eta \max = \dfrac{{m.A}}{{V.R}} \times 100\%$
Where $m.A$ is the maximum advantage of the machine . $V.R$ is the velocity ratio that is given.
So,
\eta_{\max} = \dfrac{{50}}{{100}} \times 100\% \\\ = 50\% \\\
Option A is correct.

Note :
To get the slope of the law equation of the machine, use $y = mx + c$ where assume $P$ and $W$ as
$y \\\ x$
respectively.
To get the maximum efficiency of the machine use the efficiency formula and convert into percentage.
Maximum advantage is the inverse of the slope of the machine law equation.