Water rises up to $10 \, cm$ height in a long capillary tube. If this tube is immersed in water so that the height above the water surface is only $8 \, cm$,then:

Liquid $A$ rises to a height of $10 \ cm$ in a capillary tube and liquid $B$ falls to a depth of $2 \ cm$ in the same tube. The densities of $A$ and $B$ are $1 \ g/cm^3$ and $10 \ g/cm^3$ respectively. The contact angles of $A$ and $B$ with the tube are $0^{\circ}$ and $135^{\circ}$ respectively. If the surface tensions of $A$ and $B$ are $S_A$ and $S_B$, then the ratio $\frac{S_B}{S_A}$ is:

Fill in the blanks:
$(i)$ Smaller the radius of the capillary tube,...... the height of the column. ( more / less )
$(ii)$ If the meniscus is convex,then the liquid .......... in the capillary,and if it is concave,then the liquid .......... in the capillary. ( depressed / rises up )

$A$ $U$-tube is such that the diameter of one limb is $0.4\,mm$ and that of the other is $d\,mm$. If the surface tension of water contained in the tube is $0.07\,N/m$ and the difference in the levels of liquid in the limbs is $3.6\,cm$,then the value of $d$ 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 $0.01 \times 10^{-2} \; m$)

Water rises in a capillary tube up to a height $h$. If this capillary tube is tilted by an angle of $45^o$,then the length of the water column in the capillary tube becomes