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JEE Advanced 2019Paper 1
Exam
JEE Advanced
Year
2019
Paper
Paper 1
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2019 · Paper 1 · Physics · Mechanical Properties of Fluids

A cylindrical capillary tube of 0.2mm radius is made by joining two...

A cylindrical capillary tube of 0.2mm0.2mm radius is made by joining two capillaries T1{T}_{1} and T2{T}_{2} of different materials having water contact angles of 0o{0}^{o} and 60o,{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,= 0.075N / m, density of water =1000kg/m3,= 1000kg / {m}^{3}, take g=10m/s2)g = 10m / {s}^{2} )
A cylindrical capillary tube of 0.2mm radius is made by joining two capillaries T _ 1 and T _ 2 of different materials

Options

  1. AFor case II, if the capillary joint is 5cm5cm above the water surface, the height of water column raised in the tube will be 3.75cm.3.75cm . (Neglect the weight of the water in the meniscus)
  2. BFor case I, if the joint is kept at 8cm8cm above the water surface, the height of water column in the tube will be 7.5cm.7.5cm . (Neglect the weight of the water in the meniscus)
  3. CThe 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.
  4. DFor case I, if the capillary joint is 5cm5cm above the water surface, the height of water column raised in the tube will be more than 8.75cm.8.75cm . (Neglect the weight of the water in the meniscus)

Correct answer

A. For case II, if the capillary joint is 5cm5cm above the water surface, the height of water column raised in the tube will be 3.75cm.3.75cm . (Neglect the weight of the water in the meniscus)

Step-by-step solution

Heights if only single material tubes are used of sufficient length, For table T1⇒h1=2Tcosθprg=2×0.075×cos⁡0Kd1000×2×10−4×10=7.5cm{T}_{1} ⇒ {h}_{1} = \dfrac{2Tcos\theta}{prg} = \dfrac{2 \times 0.075 \times \cos 0Kd}{1000 \times 2 \times {10}^{- 4} \times 10} = 7.5cm For table T2⇒h2=2Tcosθ′prg=2×0.075×cos⁡60°1000×2×10−4×10=3.75cm{T}_{2} ⇒ {h}_{2} = \dfrac{2Tcos{\theta}^{′}}{prg} = \dfrac{2 \times 0.075 \times \cos 60 °}{1000 \times 2 \times {10}^{- 4} \times 10} = 3.75cm Weight of water in meniscus will be different in two cases because angle of contact is different ⇒⇒\left(C\right)iscorrect.Liquidwillriseonlyuptoheightofis correct. Liquid will rise only upto height of5cmandmeniscuswilladjustbychangingisradiusofcurvature.Iftheliquidgoesupintubeand meniscus will adjust by changing is radius of curvature. If the liquid goes up in tube2thenitwillnotbeabletosupporttheweightoftheliquidthen it will not be able to support the weight of the liquid⇒ ( D )isincorrect.Foroptionis incorrect. For option( B )Referdiagrambelow−<imgsrc="https://cdn−question−pool.getmarks.app/pyq/jeeadvanced/srzppyajnsmxkbytwvuiqltfrgtukccqtwiusdozwratdimbdp.png"/>AsRefer diagram below - <img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/srzppyajnsmxkbytwvuiqltfrgtukccqtwiusdozwratdimbdp.png"/> As{K}_{4}maximumheightuptowhichliquidmayriseincapillaryismaximum height upto which liquid may rise in capillary is{h}_{1} = 7.5cmAndlengthoftubeavailableisAnd length of tube available is8cm ⇒WaterwillriseuptoWater will rise upto7.5cm ⇒ ( B )iscorrect.Foroptionis correct. For option( A ),Referfigurebelow−<imgsrc="https://cdn−question−pool.getmarks.app/pyq/jeeadvanced/tugqiehtaukdwcdodipxhcqfknxqztkvndepmfddcqgjrppqow.png"/>Heremaximumheightuptowhichwatercanriseincase−, Refer figure below - <img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/tugqiehtaukdwcdodipxhcqfknxqztkvndepmfddcqgjrppqow.png"/> Here maximum height upto which water can rise in case-2,,{h}_{2} = 3.75cm.Alsothelengthoftubeavailableis. Also the length of tube available is5cm..⇒WaterwillriseuptoWater will rise upto3.75cm ⇒ ( A ) is correct.
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