Q143 / 150 · MHT CET 2025 (25 Apr Shift 2) · Physics

When one end of a capillary tube is dipped in water, the height of water column is ' $h$ '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is (Surface tension of water $=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ )

  • Correct answer
    A
    $1 \cdot 5 \mathrm{~cm}$
  • B
    2 cm
  • C
    $2 \cdot 5 \mathrm{~cm}$
  • D
    3 cm

Solution

The upward force due to surface tension in a capillary tube is given by

$F = T L \cos\theta$

where $T$ represents surface tension, $L$ the inner circumference, and $\theta$ the angle of contact. For water in a clean glass capillary, $\theta \approx 0^\circ$, simplifying to $\cos\theta = 1$, so the relation becomes

$F = T L$

Given the upward force $F = 105\ \text{dyne}$, surface tension of water $T = 7 \times 10^{-2}\ \text{N/m}$, and the conversion $1\ \text{N} = 10^5\ \text{dyne}$, the force in SI units is

$F = 1.05 \times 10^{-3}\ \text{N}$

Solving for circumference:

$L = \frac{F}{T} = \frac{1.05 \times 10^{-3}}{7 \times 10^{-2}} = 0.015\ \text{m}$

Converting to centimeters,

$L = 1.5\ \text{cm}$

Answer: A

Hence, the correct answer is option: 'A'.

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