A capillary tube of radius 0.25 mm is submerged vertically in water so that 25 mm of its length is outside water. The radius of curvature of the meniscus will be
(surface tension of water `=75xx10^(-3)` N/m)

Options

A. 0.2 mm
B. 0.4 mm
C. 0.6 mm
D. 0.8 mm

Answer

To find the radius of curvature of the meniscus in a capillary tube submerged in water, we can use the formula derived from the principles of capillarity. Here’s a step-by-step solution:

### Step 1: Understand the problem
We have a capillary tube with a radius \( r = 0.25 \) mm submerged in water. The height of the water column above the water surface in the tube is \( h = 25 \) mm. We need to find the radius of curvature \( R \) of the meniscus formed at the water's surface inside the tube.

### Step 2: Use the formula for radius of curvature
The radius of curvature \( R \) can be calculated using the formula:
\[ R = \frac{2T}{\rho g h} \]
where:
- \( T \) is the surface tension of water,
- \( \rho \) is the density of water,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height of the water column.

### Step 3: Substitute the known values
Given:
- Surface tension \( T = 75 \times 10^{-3} \) N/m,
- Density of water \( \rho = 1000 \) kg/m³,
- Acceleration due to gravity \( g = 10 \) m/s²,
- Height \( h = 25 \) mm = \( 25 \times 10^{-3} \) m.

Now substituting these values into the formula:
\[ R = \frac{2 \times (75 \times 10^{-3})}{1000 \times 10 \times (25 \times 10^{-3})} \]

### Step 4: Simplify the expression
Calculating the denominator:
\[ 1000 \times 10 \times (25 \times 10^{-3}) = 1000 \times 10 \times 0.025 = 250 \]

Now substituting back into the equation for \( R \):
\[ R = \frac{150 \times 10^{-3}}{250} \]

### Step 5: Calculate \( R \)
Now, performing the division:
\[ R = \frac{150}{250} \times 10^{-3} = 0.6 \times 10^{-3} \text{ m} \]

### Step 6: Convert to mm
Converting meters to millimeters:
\[ R = 0.6 \text{ mm} \]

### Conclusion
The radius of curvature of the meniscus is \( R = 0.6 \) mm.

### Final Answer
The radius of curvature of the meniscus will be **0.6 mm**.

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