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Height of capillary rise when radius, surface tension, density or tilt change

This type of question, asked 5 times: 2021 Paper 18, 30 Jan 2023, 7 Apr 2025, 21 Jan 2026 S2, 22 Jan 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 18

    5
    Two narrow bores of diameter 5.0 mm5.0\text{ }mm and 8.0 mm8.0\text{ }mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T=7.3×10−2Nm−1T = 7.3 \times10^{- 2}Nm^{- 1}, angle of contact =0, g=10 ms−2= 0,\text{ }g = 10{\text{ }ms}^{- 2} and density of water =1.0×103 kg m−3= 1.0 \times10^{3}\text{ }kg{\text{ }m}^{- 3} ]

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  2. Question 2

    30 Jan 2023

    19
    The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm5\text{ }cm. If the tube is dipped in a similar manner in another liquid BB of surface tension and density double the values of liquid AA, the height of liquid column raised in liquid BB would be mm

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  3. Question 3

    7 Apr 2025

    83
    A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70dyn/cm70dyn/cm and glass water contact angle ≃0∘\simeq0^{\circ} ) with 30∘30^{\circ} inclined with vertical. The length of water risen in the capillary is ____\_\_\_\_ cm. (Take g=9.8 m/s2g = 9.8\text{ }m/s^{2} )

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  4. Question 4

    21 Jan 2026 S2

    13
    Surface tension of two liquids (having same densities), T1T_{1} and T2T_{2}, are measured using capillary rise method utilizing two tubes with inner radii of r1r_{1} and r2r_{2} where r1>r2r_{1}>r_{2}. The measured liquid heights in these tubes are h1h_{1} and h2h_{2} respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights h1h_{1} and h2h_{2} and surface tensions T1T_{1} and T2T_{2} satisfy the relation :

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  5. Question 5

    22 Jan 2026 S2

    9
    When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h . If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1%1\% each, then the height of the liquid in the tube will change by ____\_\_\_\_ %.

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