In a capillary tube, liquid rises to a height of 4 cm. In the same capillary tube, mercury falls to a depth of 3 cm. The density of liquid and mercury are 1.5 g/cc and 13.6 g/cc. Then angles of contact of liquid and mercury with the same capillary tubes are `0^(@) and 140^(@)`, respectively. What is the ratio of magnitudes of approximate surface tension of mercury and the liquid?

Explanation

To find the ratio of the magnitudes of the surface tension of mercury (Tm) and the liquid (Tl) in a capillary tube, we can use the formula for capillary rise and fall:

\[ h = \frac{2T \cos \theta}{r \rho g} \]

Where:
- \( h \) = height of liquid rise or fall
- \( T \) = surface tension of the liquid
- \( \theta \) = angle of contact
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