Final answer:
To find the length of the side of the cube, we calculate the volume of water displaced by the additional weight and use it to find the cross-sectional area of the cube. The cube's side length turns out to be approximately 3.16 m.
Step-by-step explanation:
To calculate the length of the cube, we first need to determine the volume of the cube that is submerging and emerging when the 200 kg load is removed. Since removing the load causes the cube to emerge by 2 cm, we can deduce that this 2 cm represents the change in the height of the water displaced by the cube when the load is removed. Given that water has a density of approximately 1000 kg/m³, and using the principle of buoyancy which states that the weight of the displaced water is equal to the weight of the load, we can set up the equation:
Volume of water displaced = Mass of load / Density of water
The volume of water displaced equals the cross-sectional area of the cube times the difference in emergence height (0.02 m). Therefore:
Area × 0.02 m = 200 kg / 1000 kg/m³
Solving for the area, we find that the area of one side of the cube is 10 m². Hence, the length of a side of the cube is the square root of the area:
Length of a side of the cube = √(10) = 3.162 m, approximately 3.16 m.