Question

A force of 100 N is applied on an area of $ 4{m^2} $ the pressure being applied on the area is
(A) 50 Pa
(B) 25 Pa
(C) $ 2.5Pa $
(D) 400 Pa

Answer 1

Hint: Pressure is measure of the force exerted on a unit area of a given body. Its unit is given as Newton per unit square meter. So on substituting the values in the formula for the pressure, we will get the answer.
Formula used: In this solution we will be using the following formula;
 $\Rightarrow P = \dfrac{F}{A} $ where $ P $ is the pressure exerted on a body due to a force, $ F $ is the force exerted on the body, and $ A $ is the area of which the force encompasses or area of the surface of interest.

Complete step by step solution:
During some dynamic or statics analysis especially areas like fluid mechanics, hydrodynamics and aerodynamics, when we are not interested in the force exerted on the entire surface upon, we use the concept of pressure as a measure of the force on a unit area of that surface. To say that the pressure exerted on a surface is $ X $ Pa or $ XN{m^{ - 2}} $ is to say that $ X $ amount of force is exerted on $ 1{m^2} $ of area of that surface. Similarly, for the cases where the force may actually not have encompassed an area up to $ 1{m^{ - 2}} $ , it is a measure of how much force need to be exerted on $ 1{m^2} $ area to create the same effect has it as the force has done to the smaller area. The mathematical expression for the force is given as
 $\Rightarrow P = \dfrac{F}{A} $ where $ P $ is the pressure exerted on a body due to a force, $ F $ is the force exerted on the body, and $ A $ is the area of which the force encompasses.
Hence to calculate the pressure, we insert the known values given in the question and we get
 $\Rightarrow P = \dfrac{F}{A} = \dfrac{{100}}{4} = 25N{m^{ - 2}} = 25Pa $
Hence the correct answer is B.

Note:
When we are calculating for pressure, to avoid common error, the area of the surface whose pressure we’re interested in is used even though the force does not cover the entire area. For example, a man whose hand has a surface area of $ 1{m^2} $ exerts a force of 2 N on a table of an area of $ 2{m^2} $ , the pressure on the surface is $ P = \dfrac{F}{A} = \dfrac{2}{2} = 1Pa $ . However, the pressure on his hand due to the reaction force the table exerts will be $ P = \dfrac{F}{A} = \dfrac{2}{1} = 2Pa $ .