a cube of side of 10cm and mass 0.5kg floats in a liquid without only 0.2 of its height above the liquid surface. what is the relative density of the liquid.
Vc = 10^3 = 1000 cm^3. = Vol. of the cube.
Dc = 500g/1000cm^3 = 0.5 g/cm^3. = Density of the cube.
Vcb = Dc/Dl * Vc = 0.8 * 1000 = 800 = Vol. of cube below surface,
0.5/Dl * 1000 = 800,
Dl = 0.625 g/cm^3 = Density of the liquid.
To find the relative density of the liquid, we need to consider the buoyant force acting on the cube.
The buoyant force is equal to the weight of the liquid displaced by the immersed part of the cube. When the cube floats, this buoyant force is equal to the weight of the cube.
First, let's calculate the weight of the cube. The weight of an object is given by the formula:
Weight = mass * acceleration due to gravity
Given that the mass of the cube is 0.5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the cube:
Weight of the cube = 0.5 kg * 9.8 m/s^2
Now, let's calculate the volume of the cube that is submerged in the liquid. The cube is floating with only 0.2 of its height above the liquid surface, which means the remaining 0.8 is submerged. Since the cube is a perfect cube shape, all sides have the same length. Therefore, the height of the submerged part of the cube is given by:
Height of submerged part = 10 cm * 0.8 = 8 cm = 0.08 m
Next, let's calculate the volume of the submerged part of the cube. The volume of a cube is given by:
Volume of cube = side^3
Volume of submerged part = side^3 = (10 cm)^3 = 1000 cm^3 = 0.001 m^3
Since the density of water is approximately 1000 kg/m^3, we know that the weight of the liquid displaced (buoyant force) is equal to:
Weight of liquid displaced = density of liquid * volume of submerged part
Weight of liquid displaced = 1000 kg/m^3 * 0.001 m^3
Now, we can set this equal to the weight of the cube to find the relative density of the liquid:
1000 kg/m^3 * 0.001 m^3 = 0.5 kg * 9.8 m/s^2
Simplifying this equation will give us the relative density of the liquid:
Relative density of liquid = (0.5 kg * 9.8 m/s^2) / (1000 kg/m^3 * 0.001 m^3)
Relative density of liquid ≈ 0.049
Therefore, the relative density of the liquid is approximately 0.049.