GATE 2026 CH – Question 59
When a cylindrical capillary glass tube, open at both ends, is vertically inserted in a pool of water, the water level in the tube rises to 7 cm relative to the water level outside the tube. Consider that the surface tension of water is 0.07 N m$^{-1}$ and that the contact angle of water on glass is 0°. The density of water is 1000 kg m$^{-3}$, and the local acceleration due to gravity is 10 m s$^{-2}$. The diameter of the capillary tube (in μm) is __________ (rounded off to the nearest integer).
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Correct answer: 400
Explanation
The capillary rise is $h = \frac{2\sigma\cos\theta}{\rho g r}$, so $r = \frac{2 \times 0.07 \times 1}{1000 \times 10 \times 0.07} = 2 \times 10^{-4}$ m $= 200$ µm. The diameter is $2r = 400$ µm.