When a box rests on a round sheet of wood on the ground, it exerts an average pressure $p$ on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure?
A) $2 p$
B) $p / 4$
C) $4 p$
D) $p \sqrt { 2 }$
E) $p / 2$

Question

Quizplus · Accepted Answer

Pressure is defined as force per unit area ($P = \frac{F}{A}$). When the diameter of the wood sheet is halved, its radius is also halved, and since the area of a circle is $\pi r^2$, the new area is $\frac{1}{4}$th of the original area. Given that the force (weight of the box) remains constant, reducing the area to one-fourth increases the pressure fourfold ($P_{new} = \frac{F}{A/4} = 4 \frac{F}{A} = 4P$).

When a Box Rests on a Round Sheet of Wood ppp

When a Box Rests on a Round Sheet of Wood $p$