The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid B of surface tension and density double the values of liquid A, the height of liquid column raised in liquid B would be __________ m.

Solution

Physics sir · 4 steps

Height goes as T/ρ, and doubling both leaves that ratio unchanged, so the rise stays 5 cm.

1. Jurin's law. The capillary rise depends on the surface tension T, the contact angle θ, the density ρ and the tube radius r.

   h = (2T cos θ)/(ρ g r)

2. What stays fixed. The same tube is used, so r is the same, and the liquids are taken as similar, so θ is the same. That leaves h ∝ T/ρ.
3. Compare the liquids. For liquid B, T_B/ρ_B = 2T_A/2ρ_A = T_A/ρ_A. So h_B = h_A = 5 cm.
4. So. The rise is 5 cm = 0.05 m, which is option (a).

The idea to keep. In capillarity, first write h = (2T cos θ)/(ρ g r) and see which quantities change. When T and ρ change by the same factor, the height does not change at all.

Answer from the NTA final answer key. Solution by PrepWiser.