The lower end of a glass capillary tube is dipped in water. Water rises to a height of 8 cm. The tube is then broken at a height of 6 cm. The height of water column and angle of contact will be
Answers
Answer:
Height of water column = 6 cm
The angle of contact = cos⁻¹ (3/4)
Explanation:
The initial height of the water in the capillary tube is given as, h₁ = 8 cm
Case 1:
Since the tube is broken at a height of 6 cm.
Thus, the height of the water column in the capillary tube now will be,
h₂ = 6 cm.
Case 2:
We know that,
Using the Young-Laplace capillary rise equation, we get the height of the capillary tube as,
h = [(2γ cos θ) / (ρrg)]
where
γ = liquid surface tension
ρ = liquid density
r = radius of the capillary tube
g = gravity constant
θ = contact angle
Here, the radius and content of tube is the same, therefore, γ, r, ρ, g = constant i.e.,
[h / (cosθ)] = constant
∴ (h₁ / h₂) = [(cosθ₁) / (cosθ₂)]
⇒ (h₁ / h₂) = {(cos 0°) / (cos θ₂)} …… [∵ the initial angle θ₁ = 0°]
⇒ (8/6) = [1 / (cos θ₂)]
⇒ cos θ₂ = (3/4)
⇒ θ₂ = cos⁻¹ (3/4)
Thus, the angle of contact is [cos⁻¹ (3/4)].