Question

What is the SI Unit of Pressure?
(a). Atmosphere
(b). Dyne/$c{m}^2$
(c). Pascal
(d). mm of Hg

Answer 1

Hint: Convert the mathematical formula of Pressure into basic units in the MKS system.

Complete step-by-step solution -

The International System of Units (SI) is the modern form of the metric system. It is the only system of measurement with official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units.
Second (the unit of time with the symbol s),
Meter (length, m),
Kilogram (mass, kg),
Ampere (electric current, A),
Kelvin (thermodynamic temperature, K),
Mole (amount of substance, mol)
Candela (luminous intensity, cd).
Pressure is the amount of force applied at right angles to the surface of an object per unit area. The symbol for it is p or P. Mathematically it is represented as
$$P={\displaystyle \frac{F}{A}}$$
Where:
P is the Pressure
F is the magnitude of the normal force
A is the area of the surface on contact.
To get the SI unit, we will break the formula of Pressure into basics units.
$$P={\displaystyle \frac{F}{A}}$$
As we know, force is mass times acceleration where the acceleration unit is meter/$(second{)}^2$. The units of the area would be $(meter{)}^2$.
$$P={\displaystyle \frac{ma}{A}}$$
So units of Pressure would be
$$P={\displaystyle \frac{kg.{\displaystyle \frac{m}{s^2}}}{m^2}}$$
This is equal to one Pascal. So the SI unit of pressure is Pascal. Hece, the correct option is C, i.e., Pascal.
Additional Information:
Pascal is an SI unit of Pressure in the MKS system, whereas Barye is in the CGS units. Pascal is equal to one newton per square meter, and Barye is Dyne/$c{m}^2$.
One Atmosphere is equal to 101325 Pascal.
One bar is equal to 1000000 Pascal.

Note: Students usually try to memorize the SI units, but It is a wrong way to do these types of questions. Students should only memorize the basic formulas, and they should convert the given formula into basic units to dimensional formula or SI units.