If a capillary tube of radius $1 \,mm$ is immersed in water, the mass of water rising in the capillary tube is $m$. If the radius of the capillary tube is doubled, then the mass of water that rises in the same capillary tube will be

$A$ glass rod of radius $1.0\,mm$ is inserted symmetrically into a vertical capillary tube of radius $2.0\,mm$ such that their lower ends are at the same level. This arrangement is now dipped in water. The height to which water will rise into the tube will be ...... $mm$ (Surface Tension of water $T = 75 \times 10^{-3}\,N/m$,density $\rho = 10^3\,kg/m^3$,$g = 10\,m/s^2$).

In a capillary tube of radius $R$,a straight thin metal wire of radius $r$ $(R > r)$ is inserted symmetrically,and one end of the combination is dipped vertically in water such that the lower end of the combination is at the same level. The rise of water in the capillary tube is $[T =$ surface tension of water,$\rho =$ density of water,$g =$ gravitational acceleration$]$.

Two narrow tubes of diameters $d_1$ and $d_2$ are joined together to form a $U$-tube open at both ends. If the $U$-tube contains water,the difference in water levels in the limbs is ($T$ is the surface tension of water,the angle of contact is zero,the density of water is $\rho$,and $g$ is the acceleration due to gravity).

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 $mm$)

Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio $4:3$. The rise of liquid in two capillaries is $h_1$ and $h_2$ respectively. If the surface tensions of liquids are in the ratio $6:5$,the ratio of heights $\left(\frac{h_1}{h_2}\right)$ is (Assume that their angles of contact are same).