Water rises to a height of $3 \,cm$ in a capillary tube. If the cross-sectional area of the capillary tube is reduced to $1/9$th of its initial area, then the water will rise to a height of: (in $\,cm$)

What is capillarity? Give two practical illustrations of capillarity.

Which of the following statements is false?

Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio $4:3$. If their surface tensions are in the ratio $6:5$,the ratio of heights $\left(\frac{h_1}{h_2}\right)$ of liquids in the two capillary tubes is (Their angle of contacts are same).

$A$ capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of water in the capillary tube is $5 \, g$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is ...... $g$

In a $U$-shaped tube,the radius of one limb is $2 \ mm$ and that of the other limb is $4 \ mm$. $A$ liquid of surface tension $0.03 \ Nm^{-1}$,density $1500 \ kgm^{-3}$,and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is (Acceleration due to gravity $= 10 \ ms^{-2}$) (in $mm$)