Q.A cube of wood 20cm on each side,floats in water so that 30% is above the surface of the water,and 70% is below.

i.what is the density of the wood(justify the answer)
ii.what mass of lead mass has to be placed on the top of the block of wood,so that it with just be totally submerged.
iii.what volume of lead mass has to be placed on the top of wood.so that it will just be totally submerged.
iv.instead of placing weights on the top of the wood,how much force would have to be exerted on the wood to submerge it.
densities in gm/cm3: water-1.0,Iron-7.8,lead-11.3

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To calculate the answers to these questions, we'll need to use a few principles from physics and mathematics. Specifically, the concept of density and Archimedes' principle.

i. To determine the density of the wood, we'll use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

1. The volume of the cube can be found by calculating the volume of a cube, which is the length of one side cubed: Volume = (20 cm)^3 = 8000 cm^3.

2. Since the cube floats with 30% above the water, we know that 70% of the volume is submerged. Therefore, the volume of the displaced water is 0.7 * 8000 cm^3 = 5600 cm^3.

3. The buoyant force acting on the cube is equal to the weight of the displaced water. Since the density of water is given as 1.0 g/cm^3, the weight of the displaced water is 1.0 g/cm^3 * 5600 cm^3 = 5600 g.

4. The weight of the cube is equal to the buoyant force experienced. Given that 30% of the cube is above the water, we know that the weight of the cube is 30% of the buoyant force. Therefore, the weight of the cube is 0.3 * 5600 g = 1680 g.

5. The density of an object is its mass divided by its volume. Therefore, the density of the wood cube is 1680 g / 8000 cm^3 = 0.21 g/cm^3.

ii. To calculate the mass of lead required to submerge the cube, we'll use Archimedes' principle again.

1. We know that the buoyant force acting on the lead cube must be equal to the weight of the lead cube for it to be in equilibrium.

2. We can calculate the volume of the lead cube needed to create the same buoyant force as the weight of the wood cube. This can be calculated using the formula: Volume = Weight of the wood cube / Density of lead = 1680 g / 11.3 g/cm^3 = 148.67 cm^3.

3. Since the density of the lead is given as 11.3 g/cm^3, the mass of the lead cube required to have a volume of 148.67 cm^3 can be calculated as: Mass = Density of lead * Volume = 11.3 g/cm^3 * 148.67 cm^3 = 1680.671 g.

iii. The volume of the lead mass required to submerge the wood cube completely is already calculated in the previous step. It is 148.67 cm^3.

iv. To calculate the force required to submerge the wood cube without placing weights on top, we'll again use Archimedes' principle.

1. The buoyant force acting on the cube is equal to the weight of the water displaced. Since the cube is completely submerged, the volume of the water displaced is equal to the volume of the cube itself, which is 8000 cm^3.

2. The weight of the water displaced can be calculated as the product of the density of water and the volume of water displaced: Weight = Density of water * Volume of water displaced = 1.0 g/cm^3 * 8000 cm^3 = 8000 g.

3. The force required to submerge the cube is equal to the buoyant force acting on it, which is 8000 g.

Therefore, if you want to submerge the wood cube without placing any weights on top, you would need to apply a force of 8000 g or 8000 N (since 1 g = 1 N) to overcome the buoyant force.