Question

In a single movable pulley, if the effort moves by a single distance $x$ upwards, by what height is the load raised?

& A)\dfrac{x}{2} \\\ & B)x \\\ & C)4x \\\ & D)2x \\\ \end{aligned}$$

Answer 1

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.

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 $\dfrac{x}{2}$.