Mercury has an angle of contact equal to `140^(@)` with soda lime galss. A narrow tube of radius `1.00mm` made of this glass is dipped in a through containing mercury. By what amount does the mercury dip down in the tube relative to the mercury surface outside? Surface tension of mercury at the temperature of the experiment is `0.465 Nm^(-1)`. Density of mercury = `13.6xx10^(3) kg m^(-3)`.

Explanation

To solve the problem of how much mercury dips down in a narrow tube due to surface tension and the angle of contact, we can follow these steps:

### Step 1: Identify the given values
- Angle of contact (θ) = 140°
- Radius of the tube (R) = 1.00 mm = \(1.00 \times 10^{-3}\) m
- Surface tension of mercury (S) = 0.465 N/m
- Density of mercury (ρ) = \(13.6 \times 10^{3}\) kg/m³
- Acceleration due to gravity (g) = 9.8 m/s²
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