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Q.
In a capillary tube, water rises to $3 \,mm$. The height of water that will rise in another capillary tube having one-third radius of the first is
Mechanical Properties of Fluids
Solution:
For rise in capillary, the formula is $h =\frac{2 T }{ rg }$
So, for first capillary tube $h_1=\frac{2 T}{r_1 \rho g}$
For second, $h_2=\frac{2 T}{r_2 \rho g}$
$\frac{h_1}{h_2}=\frac{r_2}{r_1} \Rightarrow \frac{3}{h_2}=\frac{r_1}{3 \times r_1}\left[r_2=\frac{r_1}{3}\right]$
$h_2=9 \,mm$