Question

A girl weighing $50kgf$ wears sandals of pencil heels of the area of cross section $1c{{m}^{2}}$, stands on a floor. An elephant weighing $2000kgf$ stands on foot in each area of cross section $25c{{m}^{2}}$, on the floor. Compare the pressure exerted by both of them.

Answer 1

Hint: The pressure exerted by a body having definite area of cross section experiencing a given amount of force can be found by dividing the force acting by the area of cross section. First of all find the pressure exerted by the girl. Then find out the pressure exerted by the elephant also. Take the ratio between them. Hope these all may help you to solve this question.

Formula used:
Pressure exerted by a body is given by,
$P=\dfrac{F}{A}$
Where $F$ be the force acting and $A$ be the area of the cross section.

Complete step-by-step answer:
First of all let us find the pressure exerted by the girl on the floor.
Here in the question, it has been given that the weight of the girl is,
$m=50kgf$
Area of cross section is mentioned as,
$A=1c{{m}^{2}}$
Let us take the acceleration due to gravity as,
$g=10m{{s}^{-2}}$
Therefore the pressure exerted by the girl on the floor is,
 ${{P}_{girl}}=\dfrac{{{F}_{girl}}}{area}=\dfrac{50\times 10}{1}=500Nc{{m}^{-2}}$
Now let us calculate the pressure exerted by the elephant also.
The mass of the elephant has been mentioned in the question as,
$m=2000kgf$
And the area of cross section is given as,
$A=25c{{m}^{2}}$
The acceleration due to gravity is taken here also as,
$g=10m{{s}^{-2}}$
Therefore the pressure exerted by the elephant will be,
${{P}_{elep}}=\dfrac{{{F}_{eleph}}}{area}=\dfrac{2000\times 10}{26}=800Nc{{m}^{-2}}$
Now let us compare both the values by taking the ratio between them. That is,
$\dfrac{{{P}_{girl}}}{{{P}_{eleph}}}=\dfrac{5}{8}$
Therefore the answer for the question is obtained.

Note: The pressure depends on the force applied and the area over which the force is experiencing. The identical force can create different pressure depending upon the area in which the pressure is felt. As the force is acting over a large area, the pressure developed will be lesser.