The mass of a stone is 15.0g when completely immersed in water and 10.0g when completely immersed in a liquid of relative density 2.0. The mass of the stone...

Answer Details

The buoyant force on an object is equal to the weight of the fluid displaced by the object. When the stone is immersed in water, the buoyant force is equal to the weight of the water that is displaced. Similarly, when the stone is immersed in the liquid of relative density 2.0, the buoyant force is equal to the weight of the liquid that is displaced. From the given information, we can calculate the volume of the stone. Let the volume of the stone be V. When completely immersed in water, the buoyant force on the stone is equal to the weight of the water displaced, which is equal to the weight of the stone in air minus the weight of the stone in water. Therefore, we have: Buoyant force = Weight of stone in air - Weight of stone in water V x density of water x g = (10.0g - 15.0g) x g V = 5.0g / (density of water x g) Similarly, when completely immersed in the liquid of relative density 2.0, we have: V x density of liquid x g = (10.0g - weight of liquid displaced) x g V x 2.0 x g = (10.0g - 15.0g) x g V = 5.0g / (2.0 x density of water x g) Since the volume of the stone is the same in both cases, we can set the two expressions for V equal to each other and solve for the density of water: 5.0g / (density of water x g) = 5.0g / (2.0 x density of water x g) density of water = 2.0 Now we can use the buoyant force equation to find the weight of the stone in air: Buoyant force = Weight of stone in air - Weight of stone in water V x density of water x g = (Weight of stone in air - 15.0g) x g Weight of stone in air = V x density of water x g + 15.0g Weight of stone in air = 5.0g + 15.0g Weight of stone in air = 20.0g Therefore, the mass of the stone in air is 20.0g. Answer: 20.0g.