Surface tension of two liquids (having same densities), T₁ and T₂, are measured using capillary rise method utilizing two tubes with inner radii of r₁ and r₂ where r₁ > r₂. The measured liquid heights in these tubes are h₁ and h₂ respectively. [Ignore the weight of the liquid above the lowest point of meniscus]. The heights h₁ and h₂ and surface tensions T₁ and T₂ satisfy the relation :

Surface tension of two liquids (having same densities), T₁ and T₂, are measured using capillary rise method utilizing two tubes with inner radii of r₁ and r₂ where r₁ > r₂. The measured liquid heights in these tubes are h₁ and h₂ respectively. [Ignore the weight of the liquid above the lowest point of meniscus]. The heights h₁ and h₂ and surface tensions T₁ and T₂ satisfy the relation :

Q. Surface tension of two liquids (having same densities), T₁ and T₂, are measured using capillary rise method utilizing two tubes with inner radii of r₁ and r₂ where r₁ > r₂. The measured liquid heights in these tubes are h₁ and h₂ respectively. [Ignore the weight of the liquid above the lowest point of meniscus]. The heights h₁ and h₂ and surface tensions T₁ and T₂ satisfy the relation :

A. \( h_1 > h_2 \) and \( T_1 = T_2 \)

B. \( h_1 < h_2 \) and \( T_1 = T_2 \)

C. \( h_1 > h_2 \) and \( T_1 < T_2 \)

D. \( h_1 = h_2 \) and \( T_1 = T_2 \)

Correct Answer: \( h_1 < h_2 \) and \( T_1 = T_2 \)

Explanation

Capillary rise is given by:

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

Both liquids have same density and measurement is done using capillary rise method. For the same liquid, surface tension remains same.

Since \( r_1 > r_2 \), and height is inversely proportional to radius,

\[ h \propto \frac{1}{r} \]

Therefore,

\[ h_1 < h_2 \]

As surface tension is an intrinsic property of liquid and densities are same,

\[ T_1 = T_2 \]

Hence, the correct relation is \( h_1 < h_2 \) and \( T_1 = T_2 \).

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