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 $cm$)

Water rises to a height of $2\, cm$ in a capillary tube. If the tube is tilted $60^{\circ}$ from the vertical,water will rise in the tube to a length of ...... $cm$.

Water rises to a height of $10$ cm in a capillary tube and mercury falls to a depth of $3.112$ cm in the same capillary tube. If the density of mercury is $13.6 \text{ g/cm}^3$ and the angle of contact for mercury is $135^o$,the ratio of surface tension of water and mercury is (Assume density of water = $1 \text{ g/cm}^3$ and angle of contact for water = $0^o$)

Water rises to a height $h$ in a capillary tube. If the length of the capillary tube above the surface of water is made less than $h,$ then

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 )

$A$ uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
$(A)$ For a given material of the capillary tube,$h$ decreases with increase in $r$.
$(B)$ For a given material of the capillary tube,$h$ is independent of $\sigma$.
$(C)$ If this experiment is performed in a lift going up with a constant acceleration,then $h$ decreases.
$(D)$ $h$ is proportional to contact angle $\theta$.