Question

A girl stands on a box having $60\,cm$ length, $40\,cm$ breadth and $20\,cm$ width in three ways. The pressure exerted by the box will be
A. Maximum when length and breadth form the base.
B. Maximum when breadth and width from the base.
C. Maximum when width and length from the base.
D. The same in all the above three cases

Answer 1

Hint- Pressure is inversely related to area. When force applied is constant the pressure will be maximum when the area is minimum. Thus if we find the sides that form the base with the minimum area we can find the answer to this question.

Complete step by step answer:
We know that the pressure is the force exerted per unit area. In equation form we can write it as
$P = \dfrac{F}{A}$
Where $P$ is the pressure, $F$ is the force acting and $A$ is the area.
It is given that the girl is standing on a box. So, here the force is provided by the weight of the girl.
For a given force pressure will be maximum when area is minimum because pressure is inversely related to area.
So, we need to find the case when the area is minimum.
It is given that the length of the box is $l = 60\,cm$ ,Breadth is $b = 40\,cm$ and width is $w = 20\,cm$.
The box can be oriented in three ways.
First way is with length and breadth forming the base.
Second way is with breadth and width forming the base.
Third way is with a width and length farming base.
Let us calculate the area of the base in each case.
When length and breadth form the base, area of base is
$A = l \times b = 60 \times 90\,c{m^2}$
$\therefore A = 2400\,c{m^2}$
When breadth and width form base
$A = b \times w = 40 \times 20\,c{m^2}$
$\therefore A = 800\,c{m^2}$
When width and length form base.
$A = w \times l = 20 \times 60\,c{m^2}$
$\therefore A = 1200\,c{m^2}$
From these three areas we can see that minimum area is formed when breadth and width form the base.

Thus, the correct answer is option B.

Note: Remember that even when the force applied is constant, Pressure varies with change in area. Pressure and area are inversely related.
$P = \dfrac{F}{A}$
Where F is the force and A is the area.
As area increases the pressure decreases and as area decreases pressure increases.