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## Homework Statement

A wooden cube is floating in water. The upper face of the cube meets the surface of a pool of water when a block with mass 0.200 kg is placed on top of the cube. When you remove the block, there's a 2 cm difference in height between the upper face and the water surface.

What's the length of the cube's edge?

Possible answers are:

(A) 9 cm

(B) 10 cm (this is the correct answer)

(C) 18 cm

(D) this problem is unsolvable without knowing the density of the wood used

## Homework Equations

$$F=mg \\

B=\rho g V$$ The length of a cube's edge is the cube root of its volume

## The Attempt at a Solution

Notice that the volume of the cube is equal to the volume of the water displaced in the first picture.

Since forces are at rest, they will sum to zero Newton. (Newton's second law)

$$\rho_{water}V_{cube}g=g(0.200\mathrm{\ kg}+\rho_{wood}V_{cube})\\

\Leftrightarrow V_{cube}=\frac{0.200 \mathrm{\ kg}}{\rho_{water}-\rho_{wood}}$$ Since the density of wood is unknown, I would suppose (D) is the correct answer.

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