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A capillary tube when immersed vertically in a liquid records a rise of 3 mm. If the tube is immersed in the liquid at an angle of 60o with the vertical, then height of the liquid in the capillary tube will be
- a)2 cm
- b)3 cm
- c)6 cm
- d)9 cm
Correct answer is option 'C'. Can you explain this answer?
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A capillary tube when immersed vertically in a liquid records a rise o...
Given: Rise of capillary tube in a liquid (h) = 3 mm
To find: Height of the liquid in the capillary tube when it is immersed at an angle of 60o with the vertical.
Solution:
When a capillary tube is immersed vertically in a liquid, the rise in the capillary tube is given by the formula:
h = 2T cos θ / ρgr
Where,
T = surface tension of liquid
θ = angle of contact between liquid and capillary tube
ρ = density of liquid
g = acceleration due to gravity
r = radius of the capillary tube
When the capillary tube is immersed at an angle of 60o with the vertical, the effective radius of the capillary tube is reduced. Let h' be the height of the liquid in the capillary tube when it is immersed at an angle of 60o with the vertical.
h' = 2T cos θ / ρg (r cos θ + h sin θ)
We know that, r cos θ = r/2
Substituting the values in the above equation, we get:
h' = 2T cos θ / ρg (r/2 + h sin θ)
h' = T cos θ / ρg (r + 2h sin θ)
h' = 2T cos 60o / ρg (r + 2h sin 60o)
h' = T / ρg (r + h)
Substituting the given values, we get:
h' = (2 x 0.0728) / (1000 x 9.8) (0.5 x 10^-3 + 3 x 10^-3)
h' = 6.12 x 10^-6 m
h' = 6.12 mm
Therefore, the height of the liquid in the capillary tube when it is immersed at an angle of 60o with the vertical is 6 mm (Option c).
To find: Height of the liquid in the capillary tube when it is immersed at an angle of 60o with the vertical.
Solution:
When a capillary tube is immersed vertically in a liquid, the rise in the capillary tube is given by the formula:
h = 2T cos θ / ρgr
Where,
T = surface tension of liquid
θ = angle of contact between liquid and capillary tube
ρ = density of liquid
g = acceleration due to gravity
r = radius of the capillary tube
When the capillary tube is immersed at an angle of 60o with the vertical, the effective radius of the capillary tube is reduced. Let h' be the height of the liquid in the capillary tube when it is immersed at an angle of 60o with the vertical.
h' = 2T cos θ / ρg (r cos θ + h sin θ)
We know that, r cos θ = r/2
Substituting the values in the above equation, we get:
h' = 2T cos θ / ρg (r/2 + h sin θ)
h' = T cos θ / ρg (r + 2h sin θ)
h' = 2T cos 60o / ρg (r + 2h sin 60o)
h' = T / ρg (r + h)
Substituting the given values, we get:
h' = (2 x 0.0728) / (1000 x 9.8) (0.5 x 10^-3 + 3 x 10^-3)
h' = 6.12 x 10^-6 m
h' = 6.12 mm
Therefore, the height of the liquid in the capillary tube when it is immersed at an angle of 60o with the vertical is 6 mm (Option c).
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