Question

Figure shows a quick return mechanism. The crank OA rotates clockwise uniformly. OA = 2 cm, OO' = 4 cm. The ratio of time for forward motion to that for return motion is

• A. 0.5
• B. 2.0
• C. $\sqrt{2}$
• D. 1

Answer 1

The correct option is B 2.0

Given, OA = 1 cm, OO' = 4 cm


$cos\frac{\alpha }{2}=\frac{O{A}^{\prime }}{O{O}^{\prime }}$
$\frac{\alpha }{2}=co{s}^{-1}\left(\frac{2}{4}\right)$
$\alpha ={120}^o$

Ratio of time of forward motion to return motion

$=\frac{{360}^o-\alpha }{\alpha }=\frac{{360}^o-{120}^o}{{120}^o}$

$=\frac{{240}^o}{{120}^o}=2$