Question

A girl of mass 40kg wears heels with an area of 1cm2 in contact with the ground is (take earth’s gravitational field strength)
A. $4 \times {10^{ - 5}}Pa$
B. \[4 \times {10^4}Pa\]
C. $4 \times {10^5}Pa$
D. $40 \times {10^5}Pa$

Answer 1

Hint: Pressure: The force exerted in per unit area is known as the pressure. The pressure is denoted by ‘P’ and the SI unit of pressure is Pascal and it is denoted by ‘Pa’.
As we know that the pressure is \[ \Rightarrow P = \dfrac{F}{a}\]

Complete step by step solution:
Given,
Mass, m=40kg
Acceleration due to earth,$g = 10m{s^{ - 2}}$
Area, $a = 1c{m^2}$
Now the force exerted is,
$ \Rightarrow F = m \times g$
\[ \Rightarrow F = 40 \times 10\]
\[ \Rightarrow F = 400N\]
Now pressure on the ground is
\[ \Rightarrow P = \dfrac{F}{a}\]
First we have to change the area in ${m^2}$
$ \Rightarrow 1m = 100cm$
$ \Rightarrow 1{m^2} = {10^4}c{m^2}$
So $1c{m^2}$in ${m^2}$is
$ \Rightarrow 1c{m^2} = {10^{ - 4}}{m^2}$
Now put in the equation
\[ \Rightarrow P = \dfrac{{400}}{{{{10}^{ - 4}}}}\]
\[ \Rightarrow P = 400 \times {10^4}\]
\[ \Rightarrow P = 40 \times {10^5}Pa\]
So the answer is (D) \[40 \times {10^5}Pa\]

Note: Pressure is inversely proportional to the area and directly proportional to the applied force. Higher the area, lower the pressure. And higher the force, higher the pressure. Air pressure supports the weight of the car. Aircrafts fly due to the air pressure of the wings. Fluid flow because of pressure difference.