$A$ glass capillary of radius $0.35 \ mm$ is inclined at $60^{\circ}$ with the vertical in water. The length of the water column in the capillary is (surface tension of water $= 7 \times 10^{-2} \ N/m$,acceleration due to gravity $g = 10 \ m/s^2$,$\cos 0^{\circ} = 1$,$\cos 60^{\circ} = 0.5$,density of water $\rho = 10^3 \ kg/m^3$) (in $cm$)

Two capillary tubes of radii $0.2 \ cm$ and $0.4 \ cm$ are dipped in the same liquid. The ratio of the heights to which the liquid will rise in the tubes is:

Two capillary tubes of different diameters are dipped in water. The rise of water is

Water rises to a height of $2 \,cm$ in a capillary tube. If the cross-sectional area of the tube is reduced to $\frac{1}{16}^{\text{th}}$ of the initial area, then water will rise to a height of: (in $\,cm$)

When a capillary tube is immersed in water vertically,water rises to a height $h$ inside the tube. If the radius of another capillary tube is $\frac{1}{3}$ that of the previous,the height to which water will rise in this tube is:

The following observations were taken for determining surface tension $T$ of water by the capillary method:
Diameter of capillary,$D = 1.25 \times 10^{-2} \; m$
Rise of water,$h = 1.45 \times 10^{-2} \; m$
Using $g = 9.80 \; m/s^2$ and the simplified relation $T = \frac{rhg}{2} \times 10^3 \; N/m$,the possible error in surface tension is ........... $\%$. (Assume the least count of the measuring instrument is $0.01 \times 10^{-2} \; m$)