From the information given, we know that Block A has a weight of 4.5 kg, which means that its mass is also 4.5 kg. We also know that Block B has a weight of 2.8 kg in air.
To find the density of Block B, we need to use the fact that the two blocks have the same volume. This means that the mass of Block B must be equal to the mass of Block A, since density is defined as mass per unit volume.
We can use the formula for the weight of an object in a fluid to find the weight of Block B in water:
Weight of Block B in water = Weight of Block B in air - Buoyant Force
The buoyant force is equal to the weight of the water displaced by Block B, which is equal to the volume of Block B multiplied by the density of water (pw = 1000 kg/m³). Since the two blocks have the same volume, we can write:
Buoyant Force = Volume x Density of water
Substituting the values given, we get:
Buoyant Force = V x pw
where V is the volume of Block B.
Now we can rewrite the formula for the weight of Block B in water as:
Weight of Block B in water = Weight of Block B in air - V x pw
Substituting the values given, we get:
Weight of Block B in water = 2.8 kg - V x 1000 kg/m³
Since the mass of Block B is equal to the mass of Block A, we know that:
Mass of Block B = 4.5 kg
Density of Block B = Mass of Block B / Volume of Block B
We can rearrange this formula to get:
Volume of Block B = Mass of Block B / Density of Block B
Substituting the values given, we get:
Volume of Block B = 4.5 kg / Density of Block B
Now we can substitute this expression for the volume of Block B into the formula for the weight of Block B in water:
2.8 kg - V x 1000 kg/m³ = 4.5 kg / Density of Block B
Multiplying both sides by Density of Block B, we get:
2.8 kg x Density of Block B - 1000 kg/m³ x 4.5 kg = 0
Solving for Density of Block B, we get:
Density of Block B = 1000 kg/m³ x 4.5 kg / 2.8 kg = 1607.14 kg/m³
Therefore, the density of Block B is approximately 1607.14 kg/m³.