Explanation:

When both the feed rate and the nose radius are doubled in a turning operation, it affects the surface finish of the workpiece. Let's analyze the effect of each parameter individually:

Effect of Doubling the Feed Rate:
- The feed rate in turning is the rate at which the cutting tool advances along the workpiece.
- Increasing the feed rate means the cutting tool moves faster, resulting in higher material removal rate.
- As the cutting tool moves faster, it may cause more vibrations and chatter, leading to a poorer surface finish.
- Therefore, doubling the feed rate generally leads to a decrease in the surface finish.

Effect of Doubling the Nose Radius:
- The nose radius in turning is the radius of the cutting tool tip that comes into contact with the workpiece.
- Increasing the nose radius means a larger contact area between the cutting tool and the workpiece.
- With a larger contact area, the cutting forces are distributed over a larger area, reducing the cutting pressure at the cutting edge.
- This reduced cutting pressure helps in reducing the chances of tool wear and work hardening, resulting in a better surface finish.
- Therefore, doubling the nose radius generally leads to an increase in the surface finish.

Combined Effect:
- When both the feed rate and the nose radius are doubled, the two effects mentioned above act simultaneously.
- The increase in surface finish due to doubling the nose radius can partially compensate for the decrease in surface finish due to doubling the feed rate.
- However, the decrease in surface finish due to the increased feed rate is generally more significant than the increase in surface finish due to the increased nose radius.
- As a result, the overall effect is a decrease in the surface finish.

Therefore, the correct answer is option 'A': The surface finish decreases by 50%.