Mercury has an angle of contact equal to \(140^\circ\) with soda-lime glass. A narrow tube of radius \(1.00~\text{mm}\) made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside?
(the surface tension of mercury at the temperature of the experiment is \(0.465~\text{N m}^{–1},\) the density of mercury is \(13.6 × 10^3~\text{kg m}^{–3}\) )
1. \(4.21~\text{mm}\)
2. \(5.34~\text{mm}\)
3. \(3.12~\text{mm}\)
4. \(6.16~\text{mm}\)