Question

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

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

Answer 1

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

Given:
Load, $L=2000\text{N}$
Movement at free end, $d_E=1\text{m}$
When free end of the rope is pulled by a distance then both the segments around pulley C will move up by half the diatance to maintain the length of the rope. So, the distance moved by the pulley $\text{C}$ will be half of the distance moved by the free end of the rope, i.e.,
$d_C=\frac{d_E}{2}$
Similarly, the distance moved by pulley $\text{B}$ will be half of the distance moved by pulley $\text{C}$, i.e.,
$d_B=\frac{d_C}{2}=\frac{d_E}{2^2}$
On substituting the values,
$d_B=\frac{1}{2^2}=\frac{1}{4}$
$⟹d_B=0.25\text{m}$