The question pertains to the crank and slotted lever mechanism (QRMM) and asks about the ratio of maximum angular velocities during the return and cutting strokes, given an obliquity ratio of 2.

Explanation and Solution:

1. Key Definitions:

   • The obliquity ratio is defined as the ratio of the time of return stroke to the time of the cutting stroke.
   • In a crank and slotted lever mechanism, the maximum angular velocity of the slotted lever during return stroke and cutting stroke is inversely proportional to the respective times.

2. Given:

   • Obliquity ratio = $\text{time of return stroke} / \text{time of cutting stroke} = 2$.
   • Thus, the time of return stroke is twice the time of the cutting stroke.

3. Relationship:

   • Angular velocity ratio is the inverse of the time ratio: $\text{Angular velocity ratio} = \frac{\omega_{\text{return}}}{\omega_{\text{cutting}}} = \frac{1}{\text{obliquity ratio}} = \frac{1}{2}.$

Correct Option: (B) $\frac{1}{2}$

This means the maximum angular velocity during the return stroke is half of that during the cutting stroke.

Would you like further clarification or examples? Here are 5 related questions:

1. What is the significance of the obliquity ratio in the design of mechanisms?
2. How do time ratios influence velocity and force distributions in mechanisms?
3. What other mechanisms use obliquity ratios for motion analysis?
4. How is the crank and slotted lever mechanism applied in real-world systems?
5. Can this analysis be extended to non-uniform speed inputs?

Tip: Always relate time ratios to angular velocity ratios inversely in similar mechanisms!