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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 60° with the vertical, then height of the liquid in the capillary tube will be
- a)2 mm
- b)3 mm
- c)6 mm
- d)9 mm
Correct answer is option 'C'. Can you explain this answer?
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Degrees with the vertical, what will be the height of the liquid column inside the tube?
We can use the concept of surface tension to solve this problem. The rise of the liquid in a capillary tube is given by the formula:
h = (2T cosθ) / (ρgr)
where h is the height of the liquid column, T is the surface tension of the liquid, θ is the contact angle between the liquid and the tube, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.
In this problem, we are given that the rise of the liquid in the vertical tube is 3 mm, so we can write:
3 = (2T cos90) / (ρgr)
Simplifying this equation, we get:
T = (3ρgr) / 2
Now, when the tube is immersed at an angle of 60 degrees with the vertical, the contact angle between the liquid and the tube will also be 60 degrees. So we can use the same formula to find the height of the liquid column in this case:
h = (2T cos60) / (ρgr)
Substituting the value of T that we just found, we get:
h = (3/4) mm
Therefore, the height of the liquid column inside the tube when it is immersed at an angle of 60 degrees with the vertical is 0.75 mm.
We can use the concept of surface tension to solve this problem. The rise of the liquid in a capillary tube is given by the formula:
h = (2T cosθ) / (ρgr)
where h is the height of the liquid column, T is the surface tension of the liquid, θ is the contact angle between the liquid and the tube, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.
In this problem, we are given that the rise of the liquid in the vertical tube is 3 mm, so we can write:
3 = (2T cos90) / (ρgr)
Simplifying this equation, we get:
T = (3ρgr) / 2
Now, when the tube is immersed at an angle of 60 degrees with the vertical, the contact angle between the liquid and the tube will also be 60 degrees. So we can use the same formula to find the height of the liquid column in this case:
h = (2T cos60) / (ρgr)
Substituting the value of T that we just found, we get:
h = (3/4) mm
Therefore, the height of the liquid column inside the tube when it is immersed at an angle of 60 degrees with the vertical is 0.75 mm.
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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 60° with the vertical, then height of the liquid in the capillary tube will bea)2 mmb)3 mmc)6 mmd)9 mmCorrect answer is option 'C'. Can you explain this answer?
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