Two capillaries are dipped in two different liquids having meniscus radius 𝑅1, 𝑅2(𝑅1 > 𝑅2) and surface Tension 𝑇1 & 𝑇2. If density of liquids are same :

Correct Option: ℎ₁ < ℎ₂ then 𝑇₁ = 𝑇₂

Explanation:

The height h of a liquid column raised in a capillary tube of meniscus radius R (or radius r of meniscus) is given by the capillary rise formula:

$h=\frac{2T}{R·\rho ·g}$

where:

• T is the surface tension of the liquid,
• R is the radius of curvature of the liquid meniscus,
• ρ is the density of the liquid, and
• g is the acceleration due to gravity.

From the given image:

We are given that:

1. The meniscus radius of the first capillary tube is greater than that of the second capillary tube, i.e., R₁ > R₂.
2. The densities of both liquids are the same, i.e., ρ₁ = ρ₂ = ρ.
3. If the surface tensions are equal, i.e., T₁ = T₂, then the height h is inversely proportional to the radius of the meniscus R:

$h\propto \frac{1}{R}$

Since R₁ > R₂, it directly follows that the height of the liquid column in the first tube will be less than that in the second tube:

$h_1<h_2$

Thus, if T₁ = T₂, then h₁ < h₂.