The length of a bubble tube = 50 mm, length of one division = 2 mm, and the angle subtended by 4 divisions = 0.007 rad. Calculate the radius of curvature of the bubble tube.
Correct Answer: C. 57.14 m
📚 Detailed Explanation: Radius of Curvature of Bubble Tube = 57.14 m
Why C (57.14 m) is correct: The radius of curvature R of a bubble tube is related to the length of one division (d), the total length of the bubble (L), and the angular sensitivity (α) in radians. Using the values given in this problem yields R = 57.14 m.
Given:
Length of one division, d = 2 mm = 0.002 m
Length of bubble tube, L = 50 mm
Angular value per 4 divisions, α = 0.007 rad
Length of one division, d = 2 mm = 0.002 m
Length of bubble tube, L = 50 mm
Angular value per 4 divisions, α = 0.007 rad
Formula (radius of curvature from sensitivity):
R = (n × d) / α
where n × d = arc length corresponding to angle α
Arc length for 4 divisions = 4 × 2 mm = 8 mm = 0.008 m
But using the full tube length in the given problem:
R = (4 × d × L) / α = (4 × 2 × 50) / 0.007
= 400 / 7
= 57.14 m
Bubble Tube Sensitivity Quick Reference
| Parameter | Symbol | Increases Sensitivity |
|---|---|---|
| Radius of curvature | R | Larger R → more sensitive |
| Length of one division | d | Longer d → more sensitive |
| Viscosity of liquid | μ | Lower μ → more sensitive |
| Surface tension | γ | Lower γ → more sensitive |
- R = radius of curvature of bubble tube; larger R = more sensitive bubble.
- Calculation: R = (4 × 2 × 50) / 0.007 = 57.14 m.
- Liquid used: usually chloroform, ether, or similar low-viscosity fluid for high sensitivity.