Question:

A cylindrical capillary tube of 0.2mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0° and 60° 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?

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)

For case I, 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)

For case II, the capacity 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)

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

Solution:

Correct option is D.
For case II, the capacity 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)
Heights if only single material tubes are used of sufficient length
h1=2Tcos θ/ρrg=2×0.075×cos 0°/1000×2×10⁻⁴×10=7.5cm
h2=2Tcos θ′/ρrg=2×0.075×cos 60°/1000×2×10⁻⁴×10=3.75cm
Therefore, option(1) is correct
(2)Liquid will rise only upto a height of 5cm and meniscus will adjust by changing is radius of curvature. If the liquid goes up in tube 2 then it will not be able to support the weight of the liquid
(3)Weight of water in meniscus will be different in two cases because angle of contact is different.