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Q. No.
Surface tension of two liquids (having same densities), \(T_1\) and \(T_2\), are measured using capillary rise method utilizing two tubes with inner radii of \(r_1\) and \(r_2\) where \(r_1>r_2\). The measured liquid heights in these tubes are \(h_1\) and \(h_2\) respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights \(h_1\) and \(h_2\) and surface tensions \(T_1\) and \(T_2\) satisfy the relation:
1. \({h}_1<{h}_2\) and \({T}_1={T}_2\)
2. \({h}_1={h}_2\) and \({T}_1={T}_2\)
3. \({h}_1>{h}_2\) and \({T}_1={T}_2\)
4. \({h}_1>{h}_2\) and \({T}_1<{T}_2\)
Subtopic:  Capillary Rise |
 84%
Level 1: 80%+
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Two liquids \(A\) and \(B\) have contact angles \(\theta_A\) and \(\theta_B,\) respectively, when placed in identical capillary tubes. If
        \(K=\dfrac{\cos\theta_A}{\cos\theta_B}\)
Which of the following statements is correct?
1. \(K\) is negative, then liquid \(A\) and liquid \(B\) have convex menisci.
2. \(K\) is zero, then the liquid \(A\) has a convex meniscus and liquid \(B\) has a concave meniscus.
3. \(K\) is negative, then the liquid \(A\) has a concave meniscus, and the liquid \(B\) has a convex meniscus.
4. \(K\) is negative, then liquid \(A\) and liquid \(B\) have concave meniscus.
Subtopic:  Capillary Rise |
 78%
Level 2: 60%+
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A capillary tube of radius \(0.1~\text{mm} \) is partly dipped in water (surface tension \(70~\text{dyne/cm} \) and glass water contact angle \(≃0^\circ\)) with \(30^\circ\) inclined with the vertical. The length of water risen in the capillary is: (in cm) (Take \(g = 9.8 ~\text{m/s}^2 \))
1. \(\dfrac{57}{2}\)

2. \(\dfrac{71}{5}\)

3. \(\dfrac{68}{5}\)

4. \(\dfrac{82}{5}\)
Subtopic:  Capillary Rise |
 52%
Level 3: 35%-60%
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Given below are two statements:
Statement -I The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement -II The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
 
1. Statement I is false but Statement II is true.
2.
Both Statement I and Statement II are false.
3.
Both Statement I and Statement II are true.
4.
Statement I is true but Statement II is false.

 
Subtopic:  Capillary Rise |
 79%
Level 2: 60%+
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Consider the two statements:
Statement I: A capillary tube is first dipped in hot water and then in cold water. The water rises higher in the hot water.
Statement II: A capillary tube is first dipped in cold water and then in hot water. The water rises higher in the cold water.
1. Statement I is correct and Statement II is incorrect.
2. Statement I is incorrect and Statement II is correct.
3. Both Statement I and Statement II are correct.
4. Both Statement I and Statement II are incorrect.
Subtopic:  Capillary Rise |
 64%
Level 2: 60%+
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Two narrow bores of diameter \(5.0 ~\text{mm}\) and \(8.0 ~\text{mm}\) 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 the two limbs of the tube?
(Take surface tension of water \(T = 7.3 × 10^{–2}~ \text {N m}^{–1} ,\) angle of contact \(= 0, g = 10 ~\text{m s}^{–2}\) and density of water \(= 1.0 × 10^3 ~\text{kg m}^{–3}\))
1. \(2.19~\text{mm}\)
2. \(4.97~\text{mm}\)
3. \(5.34~\text{mm}\)
4. \(3.62~\text{mm}\)
Subtopic:  Capillary Rise |
 72%
Level 2: 60%+
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When a long glass capillary tube of radius \(0.015~\text{cm}\) is dipped in a liquid, the liquid rises to a height of \(15~\text{cm}\) within it. If the contact angle between the liquid and glass to close to \(0^\circ\), the surface tension of the liquid, in milliNewton m–1, is nearly:\(\left[\rho_{\text {(liquid) }}=900 \mathrm{~kgm}^{-3}, \mathrm{~g}=10 \mathrm{~ms}^{-2}\right] \) 
1. \(200\)
2. \(101\)
3. \(402\)
4. \(325\)

Subtopic:  Capillary Rise |
 85%
Level 1: 80%+
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A capillary tube made of glass of radius \(0.15 ~\text{mm}\) is dipped vertically in a beaker filled with methylene iodide (surface tension  \(=0.05 ~\text{Nm}^{-1},\) density \(=667~\text{kg m}^{-3}\)) which rises to height \(h\) in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of \(60^\circ\) with one another. Then \(h\) is close to:
(take \(g = 10~\text{m/s}^2\))
1. \(0.137~\text{m}\)
2. \(0.172~ \text{m}\)
3. \(0.087 ~\text{m}\)
4. \(0.049 ~\text{m}\)

Subtopic:  Capillary Rise |
Level 3: 35%-60%
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If \(M\) is the mass of water that rises in a capillary tube of radius \(r,\) then mass of water which will rise in a capillary tube of radius \(2r\) is:
1. \(M\)
2. \(4M\)
3. \(M/2\)
4. \(2M\)

Subtopic:  Capillary Rise |
 64%
Level 2: 60%+
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