Question

A machine is used to displace a load of 200 N through 5 cm by an effort of 10 N. If efficiency of the machine is $50\%$. Find its mechanical equivalent.
A. 5
B. 20
C. 10
D. 2

Answer 1

Hint: To answer this question, use the direct formula for mechanical equivalent of a machine. Mechanical equivalent is the ratio of load to the effort of the machine. It is also defined as the ratio of the output of the machine to the input of the machine. More considerably the value of mechanical equivalence, more accessible is the work done. Substitute the values in the above-mentioned formula and find the value of mechanical equivalent.
Formula used:
$Mechanical \quad equivalent= \dfrac {Load}{Effort}$

Complete answer:
Given: Load = 200 N
            Efficiency ($\epsilon$)= $50\%$
            Effort = 10 N
            Displacement (d)= 5 cm= 0.05 m
Mechanical equivalent is given by,
$M.E= \dfrac {L}{E}$
Where, M.E is the mechanical equivalent
              L is the load of the machine
              E is the effort of the machine
Substituting values in above equation we get,
$M.E= \dfrac {200}{10}$
$\Rightarrow M.E= 20$
Thus, its mechanical equivalent is 20.

So, the correct answer is option B i.e. 20.

Note:
There are different terms related to machines which include effort, load, velocity ratio, efficiency and mechanical efficiency. So, students should have the knowledge about these terms. Load is the output of the machine whereas the effort is the input to the machine. Mechanical equivalent, efficiency and velocity ratio are interconnected to each other. Mechanical equivalent is the product of efficiency ($\eta$) and velocity ratio which is given by,
$M.E= \eta \times V.R.$
Where, M. E is the mechanical equivalent
             V.R is the velocity ratio