The atmospheric pressure at a surface depends on the height of the air column above it.

An open-ended U-tube of uniform cross-sectional area contains water (density ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ ). Initially the water level stands at $0.29 \mathrm{m}$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 \mathrm{kg} {\mathrm{m}}^{-3}$ is added to the left arm until its length is $0.1 \mathrm{m}$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is

Torricelli's barometer used mercury. Pascal duplicated it using French wine of density $984 \mathrm{kg} {\mathrm{m}}^{-3}$. The height of the wine column for normal atmospheric pressure is

During blood transfusion the needle is inserted in a vein where the gauge pressure is $2000 \mathrm{Pa}$. At what height (answer to two decimal places) must the blood container be placed so that blood may just enter the vein?

(Answer approximately to two decimal places)

(Use the density of whole blood from table).

Densities of some common fluids at STP

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

Calculate the difference $\left(h\right)$ in water levels in two communicating capillary tubes of radius $1 \mathrm{mm}$ and $1.5 \mathrm{mm}$.

(Surface tension of water is $0.07\mathrm{ }\mathrm{N} {\mathrm{m}}^{-1}$)