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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?

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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.

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