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.