A metal cube fully submerged in water shows an apparent weight of 1.9 N. When completely submerged in acetone, its apparent weight is 2.2 N. What is the length of the side of the cube? (Note: The density of water is ñ_water = 1000 kg/m³ and of acetone ñ_acetone = 784 kg/m³.) A)5.0 × 10^-2 m B)2.5 × 10^-3 m C)1.4 × 10^-4 m D)We need to know the mass of the cube to calculate the length.

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Quizplus · Accepted Answer

The apparent weight of an object submerged in a fluid is given by the weight of the object in air minus the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the object, which depends on the volume of the object and the density of the fluid. Since the volume of the cube remains constant, the difference in apparent weights in water and acetone is due to the difference in the buoyant forces, which in turn depends on the densities of the fluids.Given:- Apparent weight in water = 1.9 N- Apparent weight in acetone = 2.2 N- Density of water = 1000 kg/m³- Density of acetone = 784 kg/m³The actual weight of the cube (W) can be found by adding the buoyant force in water to its apparent weight in water, which is the same as adding the buoyant force in acetone to its apparent weight in acetone. The buoyant force is the product of the volume of the cube, the density of the fluid, and the acceleration due to gravity (g = 9.8 m/s²). Since we are not given the mass of the cube directly, we can use the relationship between the buoyant forces and the apparent weights to find the volume of the cube, and from the volume, we can calculate the length of the side of the cube.Let's denote:- V as the volume of the cube,- ρ_water as the density of water,- ρ_acetone as the density of acetone,- g as the acceleration due to gravity.The buoyant force in water is V * ρ_water * g, and in acetone, it's V * ρ_acetone * g. The difference in apparent weights is due to the difference in buoyant forces, so we can set up the equation based on the difference in buoyant forces and solve for V. Once we have V, we can find the length of a side of the cube (L) since V = L³.By solving the equations with the given densities and the difference in apparent weights, we find that the volume of the cube corresponds to a side length that matches choice A, 5.0 × 10^-2 m, without needing the mass of the cube directly. This calculation involves algebraic manipulation and substitution of the given values into the formula for buoyant force and subsequently into the formula for the volume of a cube.

A Metal Cube Fully Submerged in Water Shows an Apparent