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Physics · Mechanical Properties of Matter

JEE Advanced 2019 — Paper 1 — Question 7

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1\mathrm{T}_{1} and T2\mathrm{T}_{2} of different materials having water contact angles of 0∘0^{\circ} and 60∘60^{\circ}, 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?[0pt] [Surface tension of a water =0.075 N/m=0.075 \mathrm{~N} / \mathrm{m}, density of water =1000 kg/m3=1000 \mathrm{~kg} / \mathrm{m}^{3}, take g=10 m/s2\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2} ]

Question figure
  1. Option A:

    For case II, if the joint is kept at 8 cm above the water surface, the height of water column in the tube will be 7.5 cm . (Neglect the weight of the water in the meniscus)

    Correct
  2. Option B:

    For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm . (Neglect the weight of the water in the meniscus)

  3. Option C:

    For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm . (Neglect the weight of the water in the meniscus)

    Correct
  4. Option 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.

    Correct

Answer: A, C, D

Step-by-step solution

When T1T_{1} is in contact with water then h=2 Tcos⁡θ1rρg=7.5 cm<8 cm\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta_{1}}{\mathrm{r} \rho \mathrm{g}}=7.5 \mathrm{~cm}<8 \mathrm{~cm}.

But in option (B) height is insufficient.

When T2T_{2} is in contact with water then h=2 Tcos⁡θ2rρg=3.75 cm<5 cm\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta_{2}}{\mathrm{r} \rho \mathrm{g}}=3.75 \mathrm{~cm}<5 \mathrm{~cm}

Volume of water in the meniscus depends upon the angle of contact.

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2019
Paper
Paper 1
Subject
Physics
Chapter
Mechanical Properties of Matter
Topic
Contact Angle and Capillarity

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