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. what is the mass of the stone in air
Thank you
R.D = (M in air - M in liquid) / (M in air -M in water)
2 = (M - 10) / (M - 15)
M - 10 = 2(M - 15)
M - 10 = 2M - 30
M - 2M = -30 + 10
-M = -20
M = 20
To determine the mass of the stone in air, we need to use Archimedes' principle, which states that the buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
Step 1: Find the buoyant force in water
The buoyant force in water can be determined using the equation:
Buoyant Force = Weight of the water displaced by the stone
Since the stone is completely immersed in water, the buoyant force is equal to the weight of water displaced.
Given:
Mass of the stone in water = 15.0 grams
Density of water = 1 g/cm³ (approximately)
From the density formula, Density = Mass / Volume, we can rearrange it to find the Volume.
Volume of water displaced = Mass of the stone in water / Density of water
= 15.0 g / 1 g/cm³
= 15.0 cm³
The weight of water displaced is equal to the buoyant force, which is equal to the weight of the stone in water. Therefore, the weight of the stone in water is 15.0 grams.
Step 2: Find the buoyant force in the liquid
The buoyant force in the liquid can be determined using the equation:
Buoyant Force = Weight of the liquid displaced by the stone
Since the stone is completely immersed in the liquid, the buoyant force is equal to the weight of the liquid displaced.
Given:
Relative density of the liquid = 2.0
Density of the liquid = Relative density × Density of water
= 2.0 × 1 g/cm³
= 2.0 g/cm³
The volume of liquid displaced can be calculated in the same way as in Step 1:
Volume of liquid displaced = Mass of the stone in liquid / Density of the liquid
= 10.0 g / 2.0 g/cm³
= 5.0 cm³
The weight of liquid displaced is equal to the buoyant force, which is equal to the weight of the stone in liquid. Therefore, the weight of the stone in liquid is 10.0 grams.
Step 3: Find the mass of the stone in air
To find the mass of the stone in air, we need to subtract the buoyant force in the liquid from the buoyant force in water.
Mass of the stone in air = Mass of the stone in water - Mass of the stone in liquid
= 15.0 g - 10.0 g
= 5.0 grams
Therefore, the mass of the stone in air is 5.0 grams.
To find the mass of the stone in air, we can use the concept of buoyancy and Archimedes' principle.
Archimedes' principle states that the buoyant force exerted on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
In this case, we have two scenarios: when the stone is immersed in water and when it is immersed in a liquid of relative density 2.0. Let's calculate the density of the liquid.
The relative density of a substance is the ratio of its density to the density of water. Since the relative density of the liquid is given as 2.0, we can calculate its density as follows:
Density of liquid = Relative density × Density of water
Since the density of water is approximately 1.0 g/cm³, the density of the liquid is 2.0 g/cm³.
Now, we can calculate the buoyant force in each scenario.
1. When the stone is immersed in water:
Buoyant force in water = Weight of water displaced = Mass of water displaced × Acceleration due to gravity
We know that the buoyant force in water is equal to the weight of the stone in water, which is 15.0g. The acceleration due to gravity, g, is approximately 9.8 m/s².
So, 15.0g = Mass of water displaced × 9.8 m/s²
Rearranging the equation, we can solve for the mass of water displaced:
Mass of water displaced = 15.0g / 9.8 m/s²
2. When the stone is immersed in the liquid:
Buoyant force in liquid = Weight of liquid displaced = Mass of liquid displaced × Acceleration due to gravity
We know that the buoyant force in the liquid is equal to the weight of the stone in the liquid, which is 10.0g. The acceleration due to gravity, g, is approximately 9.8 m/s².
So, 10.0g = Mass of liquid displaced × 9.8 m/s²
Rearranging the equation, we can solve for the mass of liquid displaced:
Mass of liquid displaced = 10.0g / 9.8 m/s²
Now, let's find the mass of the stone in air using the principle of buoyancy:
Mass of stone in air = Mass of stone in water - Mass of water displaced
Mass of stone in air = 15.0g - Mass of water displaced
Substituting the value of the mass of water displaced that we found in the earlier calculation, we can determine the mass of the stone in air.
Finally, you can solve the equation and find the mass of the stone in air.