Question

The given combination of pulleys is used to lift a load of $2000\text{N}$. Find the distance traveled by the load if the pulley $\text{C}$ moves up by $1\text{m}$.

• A. $0.10\text{m}$
• B. $0.50\text{m}$
• C. $0.60\text{m}$
• D. $0.25\text{m}$

Answer 1

The correct option is D $0.25\text{m}$

Given:
Load, $L=2000\text{N}$
Distance moved by pulley $\text{C}=1\text{m}$
If pulley $\text{C}$ is moving up by $1\text{m}$, then consider the hook of pulley $\text{C}$ be the point of application of effort. If $\text{C}$ is the effort point then it has two movable pulleys that is $\text{A}$ and $\text{B}$.
So, for the given system,
$\text{VR}=2^n$
where, $n=$ number of movable pulleys
So, here $n=2$ for $\text{C}$ to be effort point.
so, $\text{VR}=2^2=4$
We know that,
$\text{VR}=\frac{d_E}{d_L}$
And here $d_E=1\text{m}$ at point $\text{C}$.
$\therefore \text{VR}=4=\frac{1}{d_L}$

$⟹d_L=0.25$
That means the load moves us by $0.25\text{m}$.