Question

A fixed and movable pulley system has $50\%$ efficiency. Find the velocity ratio of the system.

• A. $2^4$
• B. $2^2$
• C. $2^5$
• D. $2^3$

Answer 1

The correct option is D $2^3$

Given:
$\eta =50\%$
Effort $E=T$

Free body diagram of the system:

At equilibrium,
Load $L=4T$
We know that,
Mechanical advantage, $\text{MA}=\frac{\text{Load}}{\text{Effort}}$
$\text{MA}=\frac{4T}{T}=4$
Efficiency, $\eta =\frac{\text{Mechanical advantage}}{\text{Velocity ratio}}$
$\frac{50}{100}=\frac{4}{\text{VR}}$
Velocity ratio, $\text{VR}=8=2^3$