A capillary tube is dipped in water up to a depth l and the water rises to a height h

Question

A capillary tube is dipped in water up to a depth $l$ and the water rises to a height $h (< l)$ in the capillary tube. The lower end of the tube is closed now and the tube is taken out of water. When the lower end of the tube is opened now the length of the liquid column in the tube will be

TestHub · Accepted Answer

The force of surface tension of water (due to top meniscus) can lift a water column of length $h < l$ . So with the help of two surfaces (top and bottom meniscus), we will be able to hold a length $2 h$

$Δ P = 2 \times \frac{2 T}{r} = \frac{4 T}{r}$

$\frac{2 T}{r} = ρ gh$

and $Δ P = ρ {gh}^{'}$

$∴ h^{'} = 2 h$

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