Question

The resultant unbalanced force is minimum in reciprocating engines when the part of mass of reciprocating is balanced with rotating mass

• A. $\frac{2}{3}$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{1}{2}$

$\text{Let c be the fraction of mass balanced}$ $\text{Primary force balanced}=cmr{\omega }^2\cos \theta$ $\text{Primary force unbalanced}=(1-c)mr{\omega }^2\cos \theta$ $\text{Vertical component of centrifugal force which is unbalanced}=cmr{\omega }^2\sin \theta$ $\text{Resultant unbalance force}$

$=\sqrt{\left(\right(1-c)mr{\omega }^2\cos \theta {)}^2+(cmr{\omega }^2\sin \theta {)}^2}$

$\frac{df}{dc}=0\Rightarrow c=\frac{1}{2}$