Explanation:
It is given that, when a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. Let A is the area of box having radius r.
Pressure is given by, [tex]P=\dfrac{F}{A}[/tex]
[tex]P\propto \dfrac{1}{A}[/tex]
[tex]A=\pi r^2=\pi (d/2)^2[/tex]
[tex]P_1=\dfrac{4F}{\pi d_1^2}[/tex]
If the wood is replaced by a sheet that has half the diameter of the original piece,
[tex]P=\dfrac{4F}{\pi d_2^2}[/tex]
[tex]d_2=\dfrac{d_1}{2}[/tex]
[tex]P_2=4\times \dfrac{4F}{\pi d_1^2}[/tex]
[tex]P_2=4\times P_1[/tex]
So, new pressure is four times of the initial pressure. Hence, this is the required solution.
