Bubble tube sensitivity and radius A level’s bubble tube has 2 mm division spacing and a desired sensitivity of 30 seconds of arc per division. What should be the radius of curvature of the bubble tube?

Introduction / Context:
Bubble tube sensitivity links the angular tilt of the instrument to the observed movement of the bubble. Designers choose the radius of curvature of the bubble tube to achieve a target sensitivity (arcseconds per division). This question requires applying the geometrical relation between arc length and subtended angle for small angles.

Given Data / Assumptions:

• Division spacing s = 2 mm.
• Sensitivity per division α = 30 seconds of arc.
• Small-angle approximation: arc length s ≈ R * α (α in radians).

Concept / Approach:

For a circular arc bubble tube, one division movement corresponds to an angular tilt α that subtends an arc length s on the tube. The radius R is therefore R = s / α. Convert the angular sensitivity from seconds to radians before substitution.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: larger radius → higher sensitivity (more bubble travel per small angle). The computed R is consistent with typical precise level tubes (on the order of several meters to tens of meters).

Why Other Options Are Wrong:

3.44 m is too small for the stated sensitivity; 1375 m is unrealistically large; “none” is incorrect given the exact calculation.

Common Pitfalls:

Forgetting to convert seconds to radians; using chord instead of arc length; mixing millimeters and meters.

Final Answer:

13.75 m