A long glass capillary is dipped in water. It is known that water wets glass completely. The water level rises by h in the tube whose length outside water is more than h. The tube is now pushed down so that only a length h/2 is outside the water surface. The angle of contact of the water surface at the upper end of the tube will be (in deg)

Engineering

Physics

Surface Tension and Surface Energy

Capillary and Pressure Difference due to Surface Tension

Question

A long glass capillary is dipped in water. It is known that water wets glass completely. The water level rises by h in the tube whose length outside water is more than h. The tube is now pushed down so that only a length h/2 is outside the water surface. The angle of contact of the water surface at the upper end of the tube will be (in deg)

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When a capillary tube is dipped in water, the water rises to a height h due to capillary action, given by $h = \frac{2 T \cos θ}{ρ g r}$ , where θ is the contact angle. Initially, θ=0° since water wets glass completely, so cosθ=1. When the tube is pushed down so only h/2 is outside, the water cannot rise to h because the tube is not long enough. The meniscus adjusts its shape, and the contact angle increases to maintain equilibrium. The rise is now h/2, so $\frac{h}{2} = \frac{2 T \cos θ}{ρ g r}$ . Substituting the original h, we get cosθ = 1/2, so θ=60°.

Final answer: 60°