Question

A cylindrical capillary tube of $0.2mm$ radius is made by joining two capillaries $T_1$ and $T_2$ of different materials having water contact angles of $0^o$ and ${60}^o$ respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure . Which of the following option(s) is (are) correct?
[Surface tension of water = $0.075N/m$, density of water = $1000kg/m^3$, take $g=10m/s^2$]

• A. For case II, if the capillary joint is $5cm$ above the water surface, the height of water column raised in the tube will be $3.75cm$. (Neglect the weight of the water in the meniscus)
• B. For case I, if the joint is kept at $8cm$ above the water surface, the height of water column in the tube will be $7.5cm$. (Neglect the weight of the water in the meniscus)
• C. For case I, If the capillary joint is $5cm$ above the water surface, the height of water column raised in the tube will be more than $8.75cm$. (Neglect the weight of the water in the meniscus)
• D. The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.

Answer 1

Answer: (A), (B), (D)

The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.

Given,
${\theta }_1=0^o,{\theta }_2={60}^o$
So, the surface tension is given by $T=\frac{\rho grh}{2cos\theta }$
for the given hight for capillary,
$h=\frac{2Tcos\theta }{\rho rg}$

For, capillary $T_1$
$h_1=\frac{2T\cos \theta }{\rho rg}=\frac{2\times 0.075\times \cos 0^{\circ }}{1000\times 2\times {10}^{-4}\times 10}=7.5cm$

For, capillary $T_2$
$h_2=\frac{2T\cos {\theta }^{\prime }}{\rho rg}=\frac{2\times 0.075\times \cos {60}^{\circ }}{1000\times 2\times {10}^{-4}\times 10}=3.75cm$

Hence, option $A$ and $B$ are correct.

For $C:$ Angle of contact will adjust to make $h=5cm$
Hence, option C is wrong.

For $D:$ The shape of meniscus are different in the for both cases so as contact of angles are also differ. Hence, correction are different.



so, option D is correct.