The angle of contact between glass and water is $0^{\circ}$ and water rises in a glass capillary up to $6 \ cm$ (Surface tension of water is $T$). Another liquid of surface tension $2T$,angle of contact $60^{\circ}$ and relative density $2$ will rise in the same capillary up to (Given: $\cos 0^{\circ}=1, \cos 60^{\circ}=0.5$) (in $cm$)

Two narrow bores of diameters $3.0 \;mm$ and $6.0 \;mm$ are joined together to form a $U$-tube open at both ends. If the $U$-tube contains water,what is the difference (in $mm$) in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is $7.3 \times 10^{-2} \;N m^{-1}$. Take the angle of contact to be zero and density of water to be $1.0 \times 10^{3} \;kg m^{-3}$ $(g = 9.8 \;m s^{-2})$.

$A$ glass capillary tube of inner diameter $0.28 \,mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel is ............ $\times 10^3 \,N/m^2$ (surface tension of water $= 0.07 \,N/m$ and atmospheric pressure $= 10^5 \,N/m^2$).

In a capillary tube of area of cross-section '$a$',water rises to a height '$h$'. To what height will water rise in a capillary tube of area of cross-section $4a$?

Water rises to a height of $20 \ mm$ in a capillary tube. If the radius of the capillary tube is made $\frac{1}{3}rd$ of its previous value,what is the new height of the capillary rise (in $mm$)?

Water rises to a height of $10 \, cm$ in a capillary tube and mercury falls to a depth of $3.1 \, cm$ in the same capillary tube. If the density of mercury is $13.6 \, g/cm^3$ and the angle of contact for mercury is $135^{\circ}$,the approximate ratio of surface tensions of water and mercury is