To determine the events that could occur given the densities of the solids and liquids, we need to understand the floating principle. A solid will float in a liquid if its density is less than the density of the liquid, and it will sink if its density is greater than that of the liquid.
Let's analyze each of the solids and their respective conditions in the liquids:
- Density of Solid S1: [tex]\( \rho_{S1} = 0.78 \, \text{g/cm}^3 \)[/tex]
- Density of Solid S2: [tex]\( \rho_{S2} = 1.32 \, \text{g/cm}^3 \)[/tex]
- Density of Liquid L1: [tex]\( \rho_{L1} = 1.30 \, \text{g/cm}^3 \)[/tex]
- Density of Liquid L2: [tex]\( \rho_{L2} = 0.75 \, \text{g/cm}^3 \)[/tex]
Now, we evaluate the floating conditions:
1. For Solid S1:
- In Liquid L1:
- [tex]\( \rho_{S1} < \rho_{L1} \implies 0.78 \, \text{g/cm}^3 < 1.30 \, \text{g/cm}^3 \)[/tex]
- Therefore, S1 floats in L1.
- In Liquid L2:
- [tex]\( \rho_{S1} > \rho_{L2} \implies 0.78 \, \text{g/cm}^3 > 0.75 \, \text{g/cm}^3 \)[/tex]
- Therefore, S1 does not float in L2.
Hence, S1 floats in L1 and does not float in L2.
2. For Solid S2:
- In Liquid L1:
- [tex]\( \rho_{S2} > \rho_{L1} \implies 1.32 \, \text{g/cm}^3 > 1.30 \, \text{g/cm}^3 \)[/tex]
- Therefore, S2 does not float in L1.
- In Liquid L2:
- [tex]\( \rho_{S2} > \rho_{L2} \implies 1.32 \, \text{g/cm}^3 > 0.75 \, \text{g/cm}^3 \)[/tex]
- Therefore, S2 does not float in L2.
Hence, S2 does not float in either L1 or L2.
Considering these results, we evaluate the conditions given in the question:
- Condition A: S1 floats in L1 but not in L2.
- This condition is true.
- Condition B: S1 floats in both L1 and L2.
- This condition is false.
- Condition C: S2 floats in both L1 and L2.
- This condition is false.
- Condition D: S2 floats in L1 but not in L2.
- This condition is false.
Therefore, the final events that could occur given these densities are:
- A: True
- B: False
- C: False
- D: False
[tex]\[
\boxed{\text{True, False, False, False}}
\][/tex]
