Question

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?

Answer 1

Step-by-step 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,
`P=(F)/(A)`

`P\propto (1)/(A)`

`A=\pi r^2=\pi (d/2)^2`

`P_1=(4F)/(\pi d_1^2)`

If the wood is replaced by a sheet that has half the diameter of the original piece,

`P=(4F)/(\pi d_2^2)`

`d_2=(d_1)/(2)`

`P_2=4* (4F)/(\pi d_1^2)`

`P_2=4* P_1`

So, new pressure is four times of the initial pressure. Hence, this is the required solution.