Question

A combination of a movable pulley ${\text{P}}_1$​ with a fixed pulley ${\text{P}}_2$​ is used for lifting up a load W. If the free end of the string moves through a distance $\text{x}$, find the distance by which the load W is raised.

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

Answer 1

The correct option is C $\frac{\text{x}}{2}$

Considering the above figure,
The string that is moving through pulley $P_1$ and $P_2$ are same and we assume that the string is inextensible.

As the thread attached to the pulley $P_1$ 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 $P_1$ moves through a distance $\frac{\text{x}}{2}$.