Question

A combination of a movable pulley $\text{A}$​ with a fixed pulley $\text{B}$​ is used for lifting up a load $W$. If the free end of the string moves through a distance $x$, find the distance by which the load $W$ is raised.

• A. $x$
• B. $2x$
• C. $x^2$
• D. $\frac{x}{2}$

Answer 1

The correct option is D $\frac{x}{2}$

Considering the above figure,
The string that is moving through pulley $\text{A}$ and $\text{B}$ are same and we assume that the string is inextensible.

As the string attached to the pulley $\text{A}$ has to move equally on both the sides of the pulley, therefore if the free end of the string moves a distance of $x$ then the load attached to $\text{A}$ moves through a distance $\frac{x}{2}$.