Question

A force of $600\,N$ acts on the bullet of the area of cross section $0.6\,c{m^2}.$ The pressure exerted is ${10^x}$ What is $x$?

Answer 1

Hint: In order to solve this question, we should know about pressure. Pressure is the physical quantity which is defined as the force acting on a body per unit area of the surface where force is applied where force is defined as the external agent which has the ability to change the state of motion from rest to moving and moving body to rest. Here, we will use the general formula of pressure in order to calculate the value of $x$ in a given problem.

Formula Used:
Pressure Force and Area are related as:
$P = \dfrac{F}{A}$
where, $F$ is the force acting on a body and $A$ is the area of the surface and $P$ is the pressure acting on the surface.

Complete step by step answer:
According to the question, we have given these following parameters.
$A = 0.6c{m^2} = 0.6 \times {10^{ - 4}}{m^2}$ area of cross section.
$\Rightarrow f = 600\,N$ force acting on the bullet.
$\Rightarrow P = {10^x}\,N{m^{ - 2}}$ pressure acting on the bullet,
Now, using the formula $P = \dfrac{F}{A}$ and putting the values we get,
${10^x} = \dfrac{{600}}{{0.6 \times {{10}^{ - 4}}}}$
$\Rightarrow {10^x} = {10^7}$
Since base of the exponent values are same, so comparing the powers we get,
$\therefore x = 7$

Hence, the value of x is $x = 7$.

Note: It should be remembered that, basic unit of conversions are used while solving this question is $1cm = {10^{ - 2}}m$ and The standard name of SI unit of pressure is known as Pascal which is defined as the force of $1N$ acting on a surface area of $1{m^2}$ which can also be written as $1N{m^{ - 2}} = 1Pascal$ and the concept of pressure was introduced by Blaise Pascal.