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In a single movable pulley, if the effort moves by a single distance \[x\] upwards, by what height is the load raised?
\[\begin{align}
  & A)\dfrac{x}{2} \\
 & B)x \\
 & C)4x \\
 & D)2x \\
\end{align}\]

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Last updated date: 13th Jun 2024
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Answer
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Hint: We will use the mechanical advantage of pulley to determine the height of the load raised by the effort. Mechanical advantage is the amplification of forces achieved while using a particular tool. We must know that the mechanical advantage of a pulley system is directly proportional to the number of movable pulleys.

Formula used:
\[M.A.=2\times \text{Number of movable pulleys}\]

Complete step by step answer:
The system of a single movable pulley consists of one pulley which is not attached to any stationary object.
                   
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We know that mechanical advantage is a measure of how much the required force is spread through the system. Simply, it is a force multiplier because it multiplies the force we exert. The mechanical advantage of a pulley system is given as,
\[M.A.=2\times \text{Number of movable pulleys}\]
In this case, we have only one movable pulley. So the mechanical advantage off this pulley system will be,
\[M.A.=2\times 1=2\]
That means it will multiply the force we exert two times. So, if we take the particular case given in the question, we have an effort which moves by a distance \[x\]upwards. So, the height of the load raised will be,
\[\text{Distance}=\dfrac{\text{Distance of effort}}{M.A.}\]
\[d=\dfrac{x}{2}\]
So, we can conclude that the load will be raised by a distance of \[\dfrac{x}{2}\] by the effort.

Therefore option a is the right choice.

Note:
We can also solve this question by just analyzing the figure and understanding the movement of rope and the load. That is, we have a load attached to the movable pulley and a rope is fixed to the ceiling that passes through the movable pulley. Now, if we need to lift the effort through a distance of \[x\], then the load will travel a distance of \[\dfrac{x}{2}\].