Water rises to a height of $20 \ mm$ in a capillary tube. If the radius of the capillary tube is made $\frac{1}{3}rd$ of its previous value,what is the new height of the capillary rise (in $mm$)?

$A$ capillary tube of radius $r$ is immersed in a liquid and the mass of the liquid which rises up in it is $M$. If the radius of the tube is doubled,then the mass of the liquid which will rise in the capillary tube will be ............

$A$ 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 $\theta$.

When a capillary tube is dipped vertically in water,the water rises to a height of $2.0 \, cm$. If the capillary tube is tilted at an angle of $60^\circ$ with the vertical,what will be the length of the water column in the capillary tube in $cm$?

When a part of a straight capillary tube is placed vertically in a liquid, the liquid rises up to a certain height $h$. If the inner radius of the capillary tube, density of the liquid, and surface tension of the liquid decrease by $1\%$ each, then the height of the liquid in the tube will change by . . . . . . $\%$.

Mercury has an angle of contact equal to $140^{\circ}$ with soda lime glass. $A$ narrow tube of radius $1.00 \; mm$ made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down (in $mm$) in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is $0.465 \; N m^{-1}$. Density of mercury $= 13.6 \times 10^{3} \; kg m^{-3}$.