Question

A capillary tube of length $\frac{5T}{R\rho g}$ and cross-section radius $R$ contain fluid column of length $l$ where $l=\frac{3T}{R\rho g}$. This capillary tube is kept vertical. Surface tension and density of fluid are $T$ and $\rho$ respectively. Contact angle between fluid and the material of tube can be zero.

• A. Shape of meniscus is concave towards air at both top at bottom
• B. Shape of meniscus is concave towards air at top and convex towards air at bottom
• C. Radius of curvature of fluid at top is $R$
• D. Radius of curvature of fluid at bottom is $2R$

Answer 1

Answer: (B), (C), (D)

The correct options are
B Shape of meniscus is concave towards air at top and convex towards air at bottom
C Radius of curvature of fluid at top is $R$
D Radius of curvature of fluid at bottom is $2R$

Meniscus at the top has no constaints, so it will behave like normal and hence its shape will be concave towards air. As we go from point 1 to point 2 inside the liquid, pressure increases. If this increment in pressure is greater than $\frac{2T}{R}$, then the meniscus will become convex.
So increment in pressure $\rho gh=\left(\rho g\right(\frac{3T}{R\rho g})=\frac{3T}{R}$> $\frac{2T}{R}$, Hence meniscus will be convex towards air at bottom.

Since contact angle between fluid and material is zero, hence radius of curvature of fluid at top will be $R$.

For meniscus at bottom,
$P_1=P_0-\frac{2T}{R}{P}_2=P_0-\frac{2T}{R}+\rho gl=P_0-\frac{2T}{R}+\rho g\left(\frac{3T}{R\rho g}\right)=P_0+\frac{T}{R}=P_0+\frac{2T}{2R}$
Comparing with
$P_0+\frac{2T}{R_{eq}},weget{R}_{eq}=2R$