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PhysicsMultiple correct+4 / -1Question 5 of 54

JEE Advanced 2019 · Paper 1, Physics question 5

A cylindrical capillary tube of 0.2 mm 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?

[Surface tension of water = 0.075 N/m, density of water = 1000 kg/m³, take g=10 m/s2g = 10\ \mathrm{m/s^2}]

Two vertical capillary tubes dipped in water troughs. Case I: tube T1 at the bottom (in the water) with T2 joined above it. Case II: T2 at the bottom with T1 above it.
Choose one or more options
Answer and worked solution

Official answer: A, B, C

Jurin's law.
h=2Tcos⁡θρgr=2(0.075)cos⁡θ1000×10×2×10−4=0.075cos⁡θ m.h=\frac{2T\cos\theta}{\rho gr}=\frac{2(0.075)\cos\theta}{1000\times10\times2\times10^{-4}}=0.075\cos\theta\text{ m}.
This gives 7.5 cm in T1 (θ=0∘\theta=0^\circ) and 3.75 cm in T2 (θ=60∘\theta=60^\circ).

(A) The meniscus correction depends on the meniscus shape, i.e. on the contact angle of the tube it sits in. That differs between the two cases. True.

(B) In case II the lower tube is T2, where water rises only 3.75 cm, below the joint at 5 cm. True.

(C) In case I the lower tube is T1, where water rises 7.5 cm, below the joint at 8 cm. True.

(D) In case I with the joint at 5 cm, the water reaches the joint and would have to continue into T2. But T2 can only hold the column at 3.75 cm (less than 5 cm). The water stops at the joint, with its contact angle adjusting there, at 5 cm, not more than 8.75 cm. False.

(A), (B), (C)

Topics:CapillaritySurface tension
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