Height of liquid column in a capillary tube of radius 0.1 mm is 8 cm. If a new capillary tube of radius 0.05 mm is taken, then the height of the liquid column will be :-8 cm12 cm16 cm20 cm
Question
Height of liquid column in a capillary tube of radius 0.1 mm is 8 cm. If a new capillary tube of radius 0.05 mm is taken, then the height of the liquid column will be :-8 cm12 cm16 cm20 cm
Solution
To find the height of the liquid column in the new capillary tube, we can use the principle of capillary action.
The height of the liquid column in a capillary tube is inversely proportional to the radius of the tube. This means that as the radius decreases, the height of the liquid column increases.
Given that the height of the liquid column in the original capillary tube with a radius of 0.1 mm is 8 cm, we can calculate the height of the liquid column in the new capillary tube with a radius of 0.05 mm.
Using the formula for capillary action, we have:
h1 / h2 = r2 / r1
where h1 is the height of the liquid column in the original capillary tube, h2 is the height of the liquid column in the new capillary tube, r1 is the radius of the original capillary tube, and r2 is the radius of the new capillary tube.
Plugging in the given values, we have:
8 / h2 = 0.05 / 0.1
Simplifying the equation, we get:
8 / h2 = 1 / 2
Cross-multiplying, we have:
2 * 8 = h2
Therefore, the height of the liquid column in the new capillary tube is 16 cm.
So, the correct answer is 16 cm.
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