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 \( T_1 = T_2 \)
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 \( T_1 = T_2 \).