Question

A single fixed pulley of $75\%$ efficiency and a single movable pulley of $50\%$ efficiency is arranged as shown. Calculate the velocity ratio, mechanical advantage, and efficiency of this system.

• A. $2;2;50\%$
• B. $0.75;0.75;37.5\%$
• C. $2;0.75;37.5\%$
• D. $2;1;75\%$

Answer 1

The correct option is C $2;0.75;37.5\%$

Given:
Efficiency of the fixed pulley, ${\eta }_f=75\%$
Efficiency of the movable pulley, ${\eta }_m=50\%$
We know that ${\text{VR}}_f=1$ and ${\text{VR}}_m=2$
So,${\text{VR}}_c=2$
${\eta }_f=0.75=\frac{{\text{MA}}_f}{V{R}_f}=\frac{{\text{MA}}_f}{1}$
⇒${\text{MA}}_f=0.75$
Similarly, ${\eta }_m=0.5=\frac{{\text{MA}}_m}{{\text{VR}}_m}=\frac{{\text{MA}}_m}{2}$
$⟹{\text{MA}}_m=1$
So, the $\text{MA}$ for the combination, ${\text{MA}}_c={\text{MA}}_f\times {\text{MA}}_m$
$⟹{\text{MA}}_c=0.75\times 1=0.75$
Efficiency of the system, ${\eta }_c=\frac{0.75}{2}\times 100=37.5\%$