Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by `75xx10^-4` newton force due to the weight of the liquid. If the surface tension of water is `6xx`10^-2` newton/metre the inner circumference of the capillary must be:

Options

A. `1.25xx10^-3metre`
B. `0.50xx10^-2metre`
C. `6.5xx10^-2metre`
D. `12.5xx10^-2metre`

Explanation

To find the inner circumference of the capillary tube, we can follow these steps:

### Step 1: Understand the forces involved
The upward force due to surface tension in the capillary tube balances the downward force due to the weight of the water column. The formula for the upward force due to surface tension is given by:
\[ F_{\text{up}} = C \cdot S \]
where \( C \) is the circumference of the capillary tube and \( S \) is the surface tension.

### Step 2: Set up the equation
The weight of the water column can be expressed as:
\[ F_{\text{down}} = Mg \]
where \( M \) is the mass of the water column and \( g \) is the acceleration due to gravity. In this case, we are given that:
\[ F_{\text{down}} = 75 \times 10^{-4} \, \text{N} \]

Since these two forces are balanced, we can set them equal to each other:
\[ C \cdot S = 75 \times 10^{-4} \]

### Step 3: Substitute the known values
We know the surface tension \( S \) of water is:
\[ S = 6 \times 10^{-2} \, \text{N/m} \]
Now we can substitute this value into the equation:
\[ C \cdot (6 \times 10^{-2}) = 75 \times 10^{-4} \]

### Step 4: Solve for the circumference \( C \)
To find \( C \), we rearrange the equation:
\[ C = \frac{75 \times 10^{-4}}{6 \times 10^{-2}} \]

### Step 5: Simplify the expression
Now, we can simplify the right-hand side:
\[ C = \frac{75}{6} \times \frac{10^{-4}}{10^{-2}} \]
\[ C = \frac{75}{6} \times 10^{-2} \]
\[ C = 12.5 \times 10^{-2} \]

### Step 6: Final result
Thus, the inner circumference \( C \) of the capillary tube is:
\[ C = 12.5 \times 10^{-2} \, \text{m} \]
or
\[ C = 0.125 \, \text{m} \]