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A pulley system has a velocity ratio of 2 and efficiency $80\,\% $ . calculate mechanical advantage
(A) 2.4
(B) 1.6
(C) 2
(D) 2.2

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Last updated date: 20th Jun 2024
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Answer
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Hint: We will calculate the mechanical advantage of a pulley using the formula $MA = VA \times \eta $ formula. Here, MA is mechanical advantage, VA is velocity ratio and $\eta $ is efficiency.

Complete step by step answer
It is advantageous when friction is not present. When a force is applied to a pulley; the fraction by which the machine changes is known as mechanical advantage.
Ideal machine efficiency is greater than actual machines used in the real world. As the number of ropes increases less amount of mechanical work is needed to do work. As the number of rope required to pull the system is 1, then the ideal mechanical advantage of a single fixed pulley will be 1. Similarly, when 2 ropes are used to pull the load, then ideal mechanical work is 2.
We are given that velocity ratio I.e ratio of speed with which the rope is pulled is given in ratio 3
Efficiency is $80\,\% $.
It is defined as the ratio of output to input multiplied by 100.
$\eta = 0.8$
Mechanical advantage of system
$MA = VA \times \eta $
$MA = 3 \times 0.8$
$MA = 2.4$

Hence 2.4 is the mechanical advantage of the system. Option A is correct.

Note
If efficiency used is 80 instead of 0.8 then we will get a wrong solution. This is because efficiency is output to input ratio multiplied by 100. therefore, it should be divided by 100. Secondly, ideal mechanical work cannot be less than actual mechanical work.
There is no unit in mechanical advantage that is a unit-less quantity.