When a long glass capillary tube of radius $0.015 \; cm$ is dipped in a liquid,the liquid rises to a height of $15 \; cm$ within it. If the contact angle between the liquid and glass is close to $0^{\circ}$,the surface tension of the liquid,in $milliNewton \; m^{-1}$ is $.....$
$[\rho_{\text{liquid}} = 900 \; kg \; m^{-3}, g = 10 \; ms^{-2}]$ (Give answer in closest integer)

$A$ $U$-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:

Water rises to a height $3$ cm in a capillary tube. If the cross-sectional area of the capillary tube is reduced to $1/3^{rd}$ of its initial area, then water will rise to a height of:

The sap in trees,which consists mainly of water in summer,rises in a system of capillaries of radius $r = 2.5 \times 10^{-5} \ m$. The surface tension of sap is $T = 7.28 \times 10^{-2} \ N/m$ and the angle of contact is $0^{\circ}$. Does surface tension alone account for the supply of water to the top of all trees?

$A$ 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 $\theta$.

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 ...... $cm$.