An open $ U $ -tube contains mercury. When $ 11.2 \,cm $ of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial unit ?
On pouring water on left side, mercury rises $x$ $cm$ (say) from its previous level in the right limb of U-tube creating a difference of levels of mercury by $2 \,x cm$. Equating pressure at $A$ and $B,$ we get
$P_{A}=P_{B}$ $\therefore 11.2 \times 10^{-2} \times \rho_{\text {water }} \times g=2 x \times \rho_{ Hg } \times g$ $11.2 \times 10^{-2} \times 1000 \,kg / m ^{3}$ $=2 x \times 13600 \,kg / m ^{3} $ $ x =\frac{11.2 \times 10^{-2} \times 1000}{2 \times 13600} m$ $=0.41 \,cm$
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.
