NTA Abhyas JEE Main2020PhysicsMechanical Properties of FluidsPractice
A glass capillary tube is of the shape of a truncated cone with an apex angle α so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height h , where the radius of its cross-section is b . If the surface tension of water is S , its density is ρ , and its contact angle with glass is θ , then the value of h will be ( g is the acceleration due to gravit
Options
- A2 S b ρ g cos ⁡ ( θ - α )  
- B2 S b ρ g cos ⁡ θ + α
- C2 S b ρ g cos ⁡ θ - α 2
- D2 S b ρ g cos ⁡ θ + α 2
Correct answer
D. 2 S b ρ g cos ⁡ θ + α 2
Step-by-step solution
If R be the meniscus radius, ⇒ R cos ⁡ θ + α 2 = b Excess pressure on concave side of meniscus = 2 S R h ρ g = 2 S R = 2 S b cos ⁡ θ + α 2 ⇒ h = 2 S b ρ g cos ⁡ θ + α 2