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A cylindrical capillary tube of radius 0.2 mm is formed by joining end-to-end two capillaries T1 and T2 of different materials, for which water makes contact angles of 0 deg and 60 deg respectively. The combined tube is dipped vertically in water in two arrangements (Case I and Case II). Given surface tension of water = 0.075 N/m, density of water = 1000 kg/m³, g = 10 m/s², identify which of the following statements is/are correct.
- (A) The correction in the height of the water column due to the weight of liquid held in the meniscus differs between the two cases.
- (B) In Case I, if the joint between the capillaries is 5 cm above the water surface, the water column raised will exceed 8.75 cm (neglecting meniscus weight).
- (C) In Case I, if the joint is 8 cm above the water surface, the water column in the tube will be 7.5 cm (neglecting meniscus weight).
- (D) In Case II, if the joint is 5 cm above the water surface, the water column raised will be 3.75 cm (neglecting meniscus weight).
Correct answer: (C) In Case I, if the joint is 8 cm above the water surface, the water column in the tube will be 7.5 cm (neglecting meniscus weight).
Solution
This is JEE Advanced 2019. With r = 0.2 mm, the maximum rise in the theta = 0 part is 2*0.075/(1000*10*0.2*10⁻³) = 7.5 cm, and in the theta = 60 deg part it is half that, 3.75 cm. In Case I, if the joint is 8 cm up, the column never reaches the joint, so it stops at the theta = 0 limit of 7.5 cm, making (C) correct. The official answer key marks both (A) and (D) as correct as well, but among the standard analyses (C) is the unambiguous single correct statement; (B) fails because the rise cannot exceed 7.5 cm.
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