Question

Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below:
$1Pa = 1N{m^{ - 2}}$
If the mass of air at sea level is $1034gc{m^{ - 2}},$ Calculate the pressure in pascal.

Answer 1

Hint- In this question, we will use the standard unit system and convert the mass of air at sea level into SI unit of pressure. As we know, the SI equivalent of gram is Kg and the SI unit equivalent of cm is meter. Using these conversions we will convert the quantity in SI unit and will proceed accordingly to solve further.

Complete step by step solution:

It is that the pressure is calculated as force per unit area.
$pressure = \dfrac{{force}}{{area}}$
Now, we have to calculate the pressure exerted by air on the water at sea level.
It is given that the mass of the air at sea level is $1034gc{m^{ - 2}}$
To convert the above quantity into SI unit is given below
As we know that $1kg = 1000gm$ and $1m = 100cm$ , we will use this quantities for the conversion
$= \dfrac{{1034g \times 9.8m{s^{ - 2}}}}{{c{m^2}}} \times \dfrac{{1kg}}{{1000g}} \times \dfrac{{100cm}}{{1m}}$
On cancelling the similar units and it is also given that $1pascal = 1N{m^{ - 2}}$
Substituting the value, we get
$= 1.01332 \times {10^5}N{m^{ - 2}} \\\ = 1.01332 \times {10^5}Pa \\\$

Hence, the pressure in pascal is $1.01332 \times {10^5}Pa$

Note- In order to solve questions related to the conversion system, you need to learn about the fundamental units of the SI system and how to convert units from one system to another system. In the above question, we have used the conversion of m to cm and kg to gram. Similarly in other questions, we may need other conversion units like celsius to kelvin. The derived units can be obtained from the fundamental units.