To solve the problem, we need to find the relative density of the solid and the liquid based on the given weights in air, water, and another liquid. Let's break down the solution step by step.
### Step 1: Understand the Given Data
- Weight of the solid in air (W_A) = 120 g
- Weight of the solid in water (W_W) = 80 g
- Weight of the solid in the liquid (W_L) = 60 g
### Step 2: Calculate the Buoyant Force in Water
The buoyant force (B_W) acting on the solid when submerged in water can be calculated using the difference between the weight in air and the weight in water:
\[ B_W = W_A - W_W \]
\[ B_W = 120 \, \text{g} - 80 \, \text{g} = 40 \, \text{g} \]
### Step 3: Calculate the Volume of the Solid
The buoyant force is also equal to the weight of the water displaced by the solid. Since the density of water (ρ_W) is 1 g/cm³, we can express the buoyant force as:
\[ B_W = V \cdot \rho_W \]
Where V is the volume of the solid. Thus:
\[ 40 \, \text{g} = V \cdot 1 \, \text{g/cm}^3 \]
This implies:
\[ V = 40 \, \text{cm}^3 \]
### Step 4: Calculate the Density of the Solid
The density (ρ_S) of the solid can be calculated using its weight in air and its volume:
\[ \rho_S = \frac{W_A}{V} = \frac{120 \, \text{g}}{40 \, \text{cm}^3} = 3 \, \text{g/cm}^3 \]
### Step 5: Calculate the Buoyant Force in the Liquid
Similarly, we can calculate the buoyant force when the solid is submerged in the liquid:
\[ B_L = W_A - W_L \]
\[ B_L = 120 \, \text{g} - 60 \, \text{g} = 60 \, \text{g} \]
### Step 6: Calculate the Density of the Liquid
The buoyant force in the liquid is also equal to the weight of the liquid displaced by the solid:
\[ B_L = V \cdot \rho_L \]
Thus:
\[ 60 \, \text{g} = 40 \, \text{cm}^3 \cdot \rho_L \]
Solving for ρ_L gives:
\[ \rho_L = \frac{60 \, \text{g}}{40 \, \text{cm}^3} = 1.5 \, \text{g/cm}^3 \]
### Step 7: Calculate the Relative Density of the Solid
The relative density (RD_S) of the solid is given by:
\[ RD_S = \frac{\rho_S}{\rho_W} = \frac{3 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} = 3 \]
### Step 8: Calculate the Relative Density of the Liquid
The relative density (RD_L) of the liquid is given by:
\[ RD_L = \frac{\rho_L}{\rho_W} = \frac{1.5 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} = 1.5 \]
### Final Answer
The relative densities are:
- Relative density of the solid = 3
- Relative density of the liquid = 1.5
### Summary
The final answer is:
- Relative density of the solid = 3
- Relative density of the liquid = 1.5
