Levelling instruments — identify the condition(s) under which the sensitiveness of a spirit level tube (bubble tube) decreases, considering radius of curvature, tube diameter, bubble length, viscosity, and surface tension.

Introduction / Context:
In surveying and civil engineering, the spirit level (bubble tube) on a level or theodolite is designed to be sensitive so that a very small tilt of the instrument results in a noticeable movement of the bubble. Understanding what parameters increase or decrease the sensitiveness (ability to respond to small angular changes) helps in instrument selection, maintenance, and calibration.

Given Data / Assumptions:

• Sensitivity relates to the angular tilt required to move the bubble by one division.
• Tube geometry: radius of curvature (R), internal diameter, and bubble length.
• Fluid properties: viscosity (μ) and surface tension (σ) of the liquid in the tube.

Concept / Approach:

A more sensitive level shows more bubble movement for a tiny angular tilt. Geometrically, a larger radius of curvature (flatter arc) and a suitably long bubble generally increase sensitiveness, because the bubble shifts more per unit tilt. However, fluid-dynamic factors also matter: high viscosity and high surface tension resist bubble motion and slow the response, effectively reducing sensitiveness during practical use and adjustment.

Step-by-Step Solution:

Verification / Alternative check:

Instrument design texts note that for fast, sensitive bubbles, low-viscosity liquids and controlled wetting (surface tension) are preferred. Temperature control is also used to stabilize μ and σ during calibration.

Why Other Options Are Wrong:

Radius increased — generally increases sensitivity (opposite effect).
Diameter increased — design-specific; often improves rather than reduces sensitivity.
Bubble length increased — typically increases sensitivity up to design limits.

Common Pitfalls:

Confusing static geometric sensitivity with dynamic response; overlooking that fluid properties can dominate user-perceived sensitivity even if geometric sensitivity is high.

Final Answer:

both viscosity and surface tension are increased