A liquid rises to a height of 2.4 cm in a glass capillary P . Another glass capillary Q having diameter 80% of capillary P is immersed in the same liquid. The rise of liquid in capillary Q is

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The height of liquid rise in a capillary tube is given by

$h = \frac{2 T cos θ}{r ρ g}$

For the same liquid and glass interface, $h \propto \frac{1}{r}$ or $h \propto \frac{1}{D}$ , where $D$ is the diameter of the capillary tube.

Therefore, $h_{P} D_{P} = h_{Q} D_{Q}$

Given that $D_{Q} = 0.8 D_{P}$ and $h_{P} = 2.4$ cm.

$h_{Q} = h_{P} (\frac{D _{P}}{D _{Q}})$

$h_{Q} = 2.4 (\frac{D _{P}}{0.8 D _{P}})$

$h_{Q} = \frac{2.4}{0.8} = 3$ cm

Answer: 3 cm

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