The excess pressure inside

(a) a drop of mercury of radius $2 \mathrm{mm}$. say as $x N m^{-2}$

(b) a soap bubble of radius $4 \mathrm{mm}$.say as $y N m^{-2}$

(c) an air bubble of radius $4 \mathrm{mm}$, formed inside a tank of water say as $z N m^{-2}$

The surface tension of mercury, soap solution, and water are $0.465 \mathrm{N} {\mathrm{m}}^{-1}$, $0.03 \mathrm{N} {\mathrm{m}}^{-1}$ and $0.076 \mathrm{N} {\mathrm{m}}^{-1}$, respectively.

Find the value of $\frac{x}{yz}$.

Consider a small surface area of $1 {\mathrm{mm}}^2$ at the top of a mercury drop of radius $4.0 \mathrm{mm}$. Find the force exerted on this area 

(a) by the air, above it. 

(b) by the mercury, below it. 

(c) by the mercury surface in contact with it.

The atmospheric pressure is $1.0\times {10}^5 \mathrm{Pa}$ and the surface tension of mercury is $0.465 \mathrm{N} {\mathrm{m}}^{-1}$. Neglect the effect of gravity. Assume all the numbers to be exact.

The capillaries shown in the figure, have inner radii $0.5 \mathrm{mm}$, $1.0 \mathrm{mm}$ and $1.5 \mathrm{mm}$, respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is $7.5\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

A capillary tube of radius $0.50 \mathrm{mm}$ is dipped vertically in a pot of water. The difference between the pressure of the water in the tube of $5.0 \mathrm{cm}$ below the surface and the atmospheric pressure is $k \mathrm{N} {\mathrm{m}}^{-2}$. Find the value of $k$. 

It is given that the surface tension of the water is $0.075 \mathrm{N} {\mathrm{m}}^{-1}$.

A capillary tube of radius $1 \mathrm{mm}$ is kept vertical with the lower end in water.

(a) Find the height of water raised in the capillary.

(b) If the length of the capillary tube is half the answer of part (a), find the angle made by the water surface in the capillary with the wall.