In a capillary tube,water rises to $3\, mm$. The height of water that will rise in another capillary tube having one-third radius of the first is ........ $mm$.

If two glass plates are placed very close to each other in water,then there will be a force of:

Water rises to a height of $2.2 \text{ cm}$ in a glass capillary tube. The height to which the same water rises in another capillary having $\frac{1}{4}$ of the cross-sectional area is: (in $\text{ cm}$)

Three liquids have the same surface tension and densities $\rho_1, \rho_2$,and $\rho_3$ $(\rho_1 > \rho_2 > \rho_3)$. In three identical capillaries,the rise of the liquid is the same. The corresponding angles of contact $\theta_1, \theta_2$,and $\theta_3$ are related as:

If a capillary experiment is performed in a vacuum,what happens to the liquid level in the capillary tube?

$A$ 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 $\theta$.