Each half of the wooden cube will sink in water. This is because the density of wood is greater than that of water. When an object has a greater density than the fluid it is placed in, it will sink. The volume of each half of the cube is 2cm x 2cm x 1cm, which is 4cm^3. The density of wood is typically around 0.6 g/cm^3, while the density of water is 1 g/cm^3. Since the density of wood is greater than that of water, each half of the wooden cube will sink in water.
