$A$ capillary tube is immersed vertically in water,and the water rises to a height $h_1$ on the Earth's surface. When this arrangement is taken into a mine of depth $d$ below the Earth's surface,the height of the water column is $h_2$. If $R$ is the radius of the Earth,the ratio $\frac{h_2}{h_1}$ is:

The action of a nib split at the top is explained by

Two capillary tubes $P$ and $Q$ are dipped vertically in water. The height of water level in capillary tube $P$ is $\frac{2}{3}$ of the height in capillary tube $Q$. The ratio of their diameters is

$A$ 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 $\theta$.

$A$ capillary tube of radius $R$ is immersed in water and water rises in it to a height $H$. The mass of water in the capillary tube is $M$. If the radius of the tube is halved,the mass of water that will rise in the capillary tube will now be

Water rises up to a height of $4 \,cm$ in a capillary tube. The lower end of the capillary tube is at a depth of $8 \,cm$ below the water level. The mouth pressure required to blow an air bubble at the lower end of the capillary will be '$X$' $cm$ of water,where $X$ is equal to