Question

Pressure varies with force (F) as (the provided area is the same)
(A) $P \propto F$
(B) $P \propto \dfrac{1}{F}$
(C) $P \propto {F^2}$
(D) $P \propto \dfrac{1}{{{F^2}}}$

Answer 1

To mark the correct option, you should be familiar with pressure and force. The pressure is defined often in terms of area and force. The sign, $\propto$ , tells us how two or more variables are interdependent. When variables are related to the proportional sign we can conclude what effect will be on other variables when the value of a variable increases or decreases. If two variables are directly proportional to each other, then they will increase or decrease together. And if two variables are inversely proportional to each other, then the value of one variable increases when the value of others decreases or vice-versa.

Complete Step-by-step solution:
Step 1: First, let us get familiar with the terms, pressure, force, and area. A force is a push or pulls upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. Now let us understand what pressure is. We define pressure as the force exerted per unit area on an object. Mathematically, $P = F$ . Per unit area here means that the area can be taken in any unit-system but it should be 1, for example, $1m{m^2}$ , $1c{m^2}$, $1{m^2}$ , $1k{m^2}$ , etc. Eventually, the value of the pressure we will get will be in the same unit system. Now if we define pressure, in other words, we can say that the pressure is equal to the ratio of the force applied and the area on which the force is applied. Mathematically, we can write $P = \dfrac{F}{A}$ .
Step 2: Now let us see how both pressure and force are interdependent. From the above formula of the pressure, we can see that if we keep the area constant then the pressure will increase if we increase the force on the same area without changing the direction of the force. That means, the pressure is directly proportional to the force. For instance, a force applied to an area $1m{m^2}$ has a pressure that is 100 times as great as the same force applied to an area $1c{m^2}$ . That is why a sharp needle is able to poke through the skin when a small force is exerted, but applying the same force with a finger does not puncture the skin.

Note: Although the force is a vector, the pressure is a scalar. The pressure is a scalar quantity because it is defined to be proportional to the magnitude of the force acting perpendicular to the surface area. The SI unit for pressure is the Pascal ( $Pa$ ). Another unit for the pressure is $N/{m^2}$ . we have $1Pa = 1N/{m^2}$ .