Question

Given,1 pascal is equal to _______ \[N{{m}^{-2}}\].

Answer 1

Hint: We need to know the physical quantity which has the given units Pascal and the newton per meters squared. We can then possibly compare the two quantities to get the required relation between the two so as to solve the given problem.

Complete answer:
We know that to compare and find relation between two units as given in the problem, the two units should be used for the same physical quantity. Here, we are given the units Pascal and Newton per meters squared to be compared with each other.
Let us consider the first unit – Pascal. We know that it is the standard unit of measurement of Pressure. One pascal is defined as one Newton of force acting perpendicular on a unit area of a surface. We understand that the pressure is the force acting per unit area. The definition for one pascal is derived from this relation.
Now, let us consider the second unit given to us – Newton per meter squared. We know that Newton is the SI unit for force and meters squared corresponds to the square of the length, which is indeed the area. So, from this, we can conclude that the given unit Newtons per meter squared is the force acting per unit area.
We understand from our above arguments that both the units - Pascal and the newtons per meter squared are the same. In fact, one pascal is defined as one newton per meter squared.
\[\begin{align}
  & \text{Pressure, }P=\dfrac{\text{Force, }F}{\text{Area, }A} \\
 & \Rightarrow 1Pa=1N{{m}^{-2}} \\
\end{align}\]
So, we get that \[1Pa=1N{{m}^{-2}}\]. This is the required solution.

Note:
We know that the quantity Stress is also the force applied per unit area, but it is not often considered and denoted as pressure. And therefore, the unit Pascal is not very often used, even if it is considered to be the Standard International unit for stress.