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

mass does not change. Apparent mass might change.

The mass of the stone is 15g, in air, under water, or on the moon.

Mass of a particular solid in a particular fluid, air or liquid, does not change as bobpursley posted, but it does change when the fluid is changed. A stone when weighed in air, water, diesel, brine, etc would give different values because of the different densities or viscosities of the fluids. But the stone weighs the same thing in each of the fluids anywhere in the world,i.e. on the planet earth.

To find the mass of the stone in air, we can use the concept of buoyancy and relative density.

1. First, let's calculate the buoyant force acting on the stone when it is immersed in water.

Buoyant force = Weight of water displaced by the stone
Buoyant force = Mass of water displaced by the stone × Acceleration due to gravity

We know that the mass of the stone in water is 15.0g. Since the density of water is 1.0 g/cm³, the volume of water displaced by the stone can be calculated as follows:

Volume of water displaced by the stone = Mass of stone in water / Density of water
Volume of water displaced by the stone = 15.0g / 1.0 g/cm³

2. Next, let's calculate the weight of water displaced by the stone.

Weight of water displaced by the stone = Volume of water displaced by the stone × Density of water × Acceleration due to gravity

3. Now, let's calculate the relative density of the liquid in which the stone is immersed.

Relative density = Density of the liquid / Density of water
Relative density = 2.0

So, the density of the liquid can be calculated using:

Density of the liquid = Relative density × Density of water

4. Finally, we can calculate the volume of the stone in air and then find its mass.

Volume of the stone in air = Volume of water displaced by the stone × Relative density
Mass of the stone in air = Volume of the stone in air × Density of the liquid

By substituting the values, you can find the mass of the stone in air.

To find the mass of the stone in air, we can use the principle of buoyancy. When an object is immersed in a fluid, it experiences an upward force called buoyant force. This force depends on the density of the fluid and the volume of the object.

We are given that the mass of the stone is 15.0g when completely immersed in water. This means that the buoyant force acting on the stone in water is equal to the weight of the water displaced by the stone.

We can calculate the volume of water displaced by the stone using its mass and the density of water. The density of water is approximately 1g/cm³.

Density = Mass / Volume

The volume of water displaced by the stone can be calculated as:

Volume = Mass / Density = 15.0g / 1g/cm³ = 15.0 cm³

Now, let's move on to the second part of the question. We are given that the mass of the stone is 10.0g when completely immersed in a liquid with a relative density of 2.0. Relative density is the ratio of the density of the liquid to the density of water.

The density of the liquid can be calculated as:

Density of liquid = Relative density * Density of water
= 2.0 * 1g/cm³
= 2.0 g/cm³

Again, we can calculate the volume of liquid displaced by the stone using its mass and the density of the liquid:

Volume = Mass / Density = 10.0g / 2.0g/cm³ = 5.0 cm³

Since the stone displaces the same volume of water and liquid, we can conclude that the volume of the stone is 15.0 cm³.

Now, we can calculate the mass of the stone in air. The mass in air is given by:

Mass in air = Mass in water - Mass of water = 15.0g - 15.0g = 0.0g

Therefore, the mass of the stone in air is 0.0g.