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Properties of Matter question

2023 · 30 Jan · Shift 1 · Q41
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Properties of Matter question

2023 · 30 Jan · Shift 1 · Q41

JEE MainPhysicsProperties of MatterMCQ+4 / −1
The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, 5 cm5 \mathrm{~cm}5 cm. If the tube is dipped in a similar manner in another liquid B\mathrm{B}B of surface tension and density double the values of liquid A\mathrm{A}A, the height of liquid column raised in liquid B\mathrm{B}B would be ‾\underline{\hspace{2cm}}​ m.
  1. A
    0.05
  2. B
    0.20
  3. C
    0.5
  4. D
    0.10
View written solutionFree

Correct answer: A

  1. Use the formula for capillary rise

For a liquid rising in a capillary tube,

h=2Tcos⁡θρgrh = \frac{2T\cos\theta}{\rho g r}h=ρgr2Tcosθ​

where:

  • TTT = surface tension
  • ρ\rhoρ = density of liquid
  • rrr = radius of capillary
  • θ\thetaθ = angle of contact

Since the tube is used in a similar manner for both liquids, we take rrr, ggg, and θ\thetaθ to be the same.

Thus,

h∝Tρh \propto \frac{T}{\rho}h∝ρT​

  1. Compare liquids A and B

Given for liquid B:

  • surface tension is double that of A: TB=2TAT_B = 2T_ATB​=2TA​
  • density is double that of A: ρB=2ρA\rho_B = 2\rho_AρB​=2ρA​

So,

hBhA=TB/ρBTA/ρA=2TA/2ρATA/ρA=1\frac{h_B}{h_A} = \frac{T_B/\rho_B}{T_A/\rho_A} = \frac{2T_A/2\rho_A}{T_A/\rho_A} = 1hA​hB​​=TA​/ρA​TB​/ρB​​=TA​/ρA​2TA​/2ρA​​=1

Hence,

hB=hA=5 cmh_B = h_A = 5\text{ cm}hB​=hA​=5 cm

  1. Convert to metres

5 cm=0.05 m5\text{ cm} = 0.05\text{ m}5 cm=0.05 m

  1. Select the correct option

Therefore, the height in liquid B is

0.05 m\boxed{0.05\text{ m}}0.05 m​

So the correct option is A.

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