Water rises to a height of 20 mm in a capillary. If the radius of the capillary is made 1/3 rd of its previous value, to what height will the water now rise in the tube?a)60 mmb)80 mmc)40 mmd)30 mmCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Answer

Answer

Given:
- The water rises to a height of 20 mm in a capillary.
- The radius of the capillary is reduced to 1/3 rd of its previous value.

To find:
- The new height to which the water will rise in the tube.

Assumption:
- We assume that the radius of the capillary is the only factor affecting the height to which the water rises.

Solution:
Step 1: Understanding the concept
When a liquid rises in a capillary tube, it is due to the phenomenon of capillary action. The height to which the liquid rises depends on the balance between the adhesive forces (between the liquid and the tube) and the cohesive forces (within the liquid itself).

Step 2: Applying the formula
The height to which the liquid rises in a capillary tube is given by the formula:

h = (2Tcosθ) / (ρrg)

Where:
- h is the height to which the liquid rises
- 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
- r is the radius of the capillary
- g is the acceleration due to gravity

Step 3: Solving the problem
Let's assume that the original radius of the capillary tube is r. According to the given information, the radius is reduced to 1/3 rd of its previous value, which means the new radius is r/3.

Let the original height of the water rise be h1 and the new height be h2.

Using the formula mentioned in step 2, we can write:
h1 = (2Tcosθ) / (ρrg) (1)
h2 = (2Tcosθ) / (ρrg/3) (2)

Now, we need to find the ratio of h2 to h1:
(h2/h1) = (2Tcosθ) / (ρrg/3) / (2Tcosθ) / (ρrg)
(h2/h1) = (3) / (1/3)
(h2/h1) = 9

Therefore, the new height to which the water will rise in the capillary is 9 times the original height. Since the original height is 20 mm, the new height will be:
h2 = 9 * h1 = 9 * 20 mm = 180 mm

Step 4: Answer
The water will now rise to a height of 180 mm in the capillary.
Therefore, the correct option is (a) 60 mm.

Answer

Answer

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