Question

How is the mechanical advantage related with the velocity ratio for an actual machine? State whether the efficiency of such a machine is equal to 1, less than 1, or more than 1?
A. \[M.A. > V.R.\], less than 1
B. \[M.A. = V.R.\], equal to 1
C. \[M.A. < V.R.\], less than 1
D. \[M.A. < V.R.\], more than 1

Answer 1

Hint:To solve this problem we need to use the relation between efficiency, mechanical advantage and velocity ratio. This relation is stated as the efficiency of a machine is the ratio of mechanical advantage to the velocity ratio of the machine. Along with this, we also have to consider the energy losses which take place in the actual machine which ultimately affects its efficiency.

Formula used:
$\eta = \dfrac{{M.A.}}{{V.R.}}$
where, $\eta $ is the efficiency of the machine, $M.A.$ is the mechanical advantage of the machine and $V.R.$ is the velocity ratio of the machine

Complete step by step answer:
We know that the efficiency of the machine is given by the formula $\eta = \dfrac{{M.A.}}{{V.R.}}$.
In the case of an ideal machine, the efficiency is $100\% $because there are no energy losses.Therefore, the efficiency of the ideal machine will be,
$\eta = \dfrac{{M.A.}}{{V.R.}} = 1$
$ \Rightarrow M.A. = V.R.$
However, in the case of an actual machine, it is not possible to have $100\% $ efficiency because there are always some energy losses because of the moving parts of the machine. Therefore, the efficiency of the actual machine is always less than 1.
$
\eta < 1 \\
\Rightarrow \dfrac{{M.R.}}{{V.R.}} < 1 \\
\therefore M.R. < V.R. \\ $
Thus, for an actual machine, the mechanical advantage is always less than the velocity ratio and its efficiency is always less than 1.

Thus, Option C is the right answer.

Note:We have used the term mechanical advantage of the machine. Generally, mechanical advantage is used to analyze forces in simple machines like pulleys and levers. It is defined as the measure of the ratio of the 0utput force to the input force in the system.