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 the tube relative to the mercury surface outside, we can use the concept of capillarity and the balance of pressures due to surface tension and hydrostatic pressure.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Angle of contact (θ) = 140°
- Radius of the tube (r) = 1.00 mm = 1.00 × 10^(-3) m
- Surface tension of mercury (S) = 0.465 N/m
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