A cylindrical capillary tube of 0.2 m m radius is made by joining two capillaries T 1 and T 2 of different…

1. For case II, if the capillary joint is $5\mathrm{ }\mathrm{c}\mathrm{m}$ above the water surface, the height of water column raised in the tube will be $3.75\mathrm{ }\mathrm{c}\mathrm{m}.$ (Neglect the weight of the water in the meniscus)
2. For case I, if the joint is kept at $8\mathrm{ }\mathrm{c}\mathrm{m}$ above the water surface, the height of water column in the tube will be $7.5\mathrm{ }\mathrm{c}\mathrm{m}.$ (Neglect the weight of the water in the meniscus)
3. 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.
4. For case I, if the capillary joint is $5\mathrm{ }\mathrm{c}\mathrm{m}$ above the water surface, the height of water column raised in the tube will be more than $8.75\mathrm{ }\mathrm{c}\mathrm{m}.$ (Neglect the weight of the water in the meniscus)

Solution

Heights if only single material tubes are used of sufficient length, For table $T_1\Rightarrow h_1=\frac{2T\mathrm{c}\mathrm{o}\mathrm{s}\theta }{prg}=\frac{2\times 0.075\times \mathrm{c}\mathrm{o}\mathrm{s}0Kd}{1000\times 2\times {10}^{-4}\times 10}=7.5\mathrm{c}\mathrm{m}$ For table $T_2\Rightarrow h_2=\frac{2T\mathrm{c}\mathrm{o}\mathrm{s}{\theta }^{\prime }}{prg}=\frac{2\times 0.075\times \mathrm{c}\mathrm{o}\mathrm{s}60°}{1000\times 2\times {10}^{-4}\times 10}=3.75\mathrm{c}\mathrm{m}$ Weight of water in meniscus will be different in two cases because angle of contact is different $\Rightarrow \left(\mathrm{C}\right)$ is correct. Liquid will rise only upto height of $5\mathrm{ }\mathrm{c}\mathrm{m}$ 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 $\Rightarrow \left(\mathrm{D}\right)$ is incorrect. For option $\left(\mathrm{B}\right)$ Refer diagram below - As $K_4$ maximum height upto which liquid may rise in capillary is $h_1=7.5\mathrm{c}\mathrm{m}$ And length of tube available is $8\mathrm{ }\mathrm{c}\mathrm{m}$ $\Rightarrow$ Water will rise upto $7.5\mathrm{ }\mathrm{c}\mathrm{m}$ $\Rightarrow \left(\mathrm{B}\right)$ is correct. For option $\left(\mathrm{A}\right)$ , Refer figure below - Here maximum height upto which water can rise in case- $2$ , $h_2=3.75\mathrm{c}\mathrm{m}$ . Also the length of tube available is $5\mathrm{ }\mathrm{c}\mathrm{m}$ . $\Rightarrow$ Water will rise upto $3.75\mathrm{c}\mathrm{m}$ $\Rightarrow \left(\mathrm{A}\right)$ is correct. .

Asked in: JEE Advanced 2019 (Paper 1)

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