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 ........ $mm$.

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

If a capillary experiment is performed in a vacuum,what happens to the liquid level in the capillary tube?

$A$ capillary tube is dipped in water and it is $20 \, cm$ outside water. The water rises up to $8 \, cm$. If the entire arrangement is put in a freely falling elevator,the length of the water column in the capillary tube will be ........ $cm$.

The radii of the two columns in a $U$ tube are $r_1$ and $r_2$. When a liquid of density $\rho$ (angle of contact is $0^o$) is filled in it,the level difference of liquid in the two arms is $h$. The surface tension of the liquid is ($g =$ acceleration due to gravity):

$A$ capillary tube is immersed vertically in water,and the water rises to a height $h_1$ on the Earth's surface. When this arrangement is taken into a mine of depth $d$ below the Earth's surface,the height of the water column is $h_2$. If $R$ is the radius of the Earth,the ratio $\frac{h_2}{h_1}$ is: