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Sagot :
To determine which events could occur given the densities of the solids and liquids, we'll need to understand the concept of flotation. A substance will float in a liquid if its density is less than the density of the liquid.
Given the densities:
- [tex]\(S1 = 0.78 \, \text{g/cm}^3\)[/tex]
- [tex]\(S2 = 1.32 \, \text{g/cm}^3\)[/tex]
- [tex]\(L1 = 1.30 \, \text{g/cm}^3\)[/tex]
- [tex]\(L2 = 0.75 \, \text{g/cm}^3\)[/tex]
We'll analyze the floating conditions for these solids in the given liquids one by one.
### Analysis for S1:
1. S1 in L1:
- Density of [tex]\(S1\)[/tex] is [tex]\(0.78 \, \text{g/cm}^3\)[/tex] which is less than the density of [tex]\(L1\)[/tex] ([tex]\(1.30 \, \text{g/cm}^3\)[/tex]).
- Therefore, S1 will float in L1.
2. S1 in L2:
- Density of [tex]\(S1\)[/tex] is [tex]\(0.78 \, \text{g/cm}^3\)[/tex], which is greater than the density of [tex]\(L2\)[/tex] ([tex]\(0.75 \, \text{g/cm}^3\)[/tex]).
- Therefore, S1 will not float in L2.
### Analysis for S2:
1. S2 in L1:
- Density of [tex]\(S2\)[/tex] is [tex]\(1.32 \, \text{g/cm}^3\)[/tex], which is greater than the density of [tex]\(L1\)[/tex] ([tex]\(1.30 \, \text{g/cm}^3\)[/tex]).
- Therefore, S2 will not float in L1.
2. S2 in L2:
- Density of [tex]\(S2\)[/tex] is [tex]\(1.32 \, \text{g/cm}^3\)[/tex], which is greater than the density of [tex]\(L2\)[/tex] ([tex]\(0.75 \, \text{g/cm}^3\)[/tex]).
- Therefore, S2 will not float in L2.
Now, let's check each condition in the question:
1. Condition A: S1 floats in L1 but not in L2.
- According to the analysis, [tex]\(S1\)[/tex] does float in L1 and does not float in L2. Therefore, Condition A is True.
2. Condition B: S1 floats in both L1 and L2.
- According to the analysis, [tex]\(S1\)[/tex] does float in L1 but does not float in L2. Therefore, Condition B is False.
3. Condition C: S2 floats in both L1 and L2.
- According to the analysis, [tex]\(S2\)[/tex] does not float in L1 and does not float in L2. Therefore, Condition C is False.
4. Condition D: S2 floats in L1 but not in L2.
- According to the analysis, [tex]\(S2\)[/tex] does not float in L1 and does not float in L2. Therefore, Condition D is False.
### Conclusion
So, based on the densities provided, the events that could occur are:
- [tex]\(A\)[/tex] S1 floats in L1 but not in L2. (True)
- [tex]\(B\)[/tex] S1 floats in both L1 and L2. (False)
- [tex]\(C\)[/tex] S2 floats in both L1 and L2. (False)
- [tex]\(D\)[/tex] S2 floats in L1 but not in L2. (False)
Therefore, the correct answer is:
```
A: (True, False, False, False)
```
Given the densities:
- [tex]\(S1 = 0.78 \, \text{g/cm}^3\)[/tex]
- [tex]\(S2 = 1.32 \, \text{g/cm}^3\)[/tex]
- [tex]\(L1 = 1.30 \, \text{g/cm}^3\)[/tex]
- [tex]\(L2 = 0.75 \, \text{g/cm}^3\)[/tex]
We'll analyze the floating conditions for these solids in the given liquids one by one.
### Analysis for S1:
1. S1 in L1:
- Density of [tex]\(S1\)[/tex] is [tex]\(0.78 \, \text{g/cm}^3\)[/tex] which is less than the density of [tex]\(L1\)[/tex] ([tex]\(1.30 \, \text{g/cm}^3\)[/tex]).
- Therefore, S1 will float in L1.
2. S1 in L2:
- Density of [tex]\(S1\)[/tex] is [tex]\(0.78 \, \text{g/cm}^3\)[/tex], which is greater than the density of [tex]\(L2\)[/tex] ([tex]\(0.75 \, \text{g/cm}^3\)[/tex]).
- Therefore, S1 will not float in L2.
### Analysis for S2:
1. S2 in L1:
- Density of [tex]\(S2\)[/tex] is [tex]\(1.32 \, \text{g/cm}^3\)[/tex], which is greater than the density of [tex]\(L1\)[/tex] ([tex]\(1.30 \, \text{g/cm}^3\)[/tex]).
- Therefore, S2 will not float in L1.
2. S2 in L2:
- Density of [tex]\(S2\)[/tex] is [tex]\(1.32 \, \text{g/cm}^3\)[/tex], which is greater than the density of [tex]\(L2\)[/tex] ([tex]\(0.75 \, \text{g/cm}^3\)[/tex]).
- Therefore, S2 will not float in L2.
Now, let's check each condition in the question:
1. Condition A: S1 floats in L1 but not in L2.
- According to the analysis, [tex]\(S1\)[/tex] does float in L1 and does not float in L2. Therefore, Condition A is True.
2. Condition B: S1 floats in both L1 and L2.
- According to the analysis, [tex]\(S1\)[/tex] does float in L1 but does not float in L2. Therefore, Condition B is False.
3. Condition C: S2 floats in both L1 and L2.
- According to the analysis, [tex]\(S2\)[/tex] does not float in L1 and does not float in L2. Therefore, Condition C is False.
4. Condition D: S2 floats in L1 but not in L2.
- According to the analysis, [tex]\(S2\)[/tex] does not float in L1 and does not float in L2. Therefore, Condition D is False.
### Conclusion
So, based on the densities provided, the events that could occur are:
- [tex]\(A\)[/tex] S1 floats in L1 but not in L2. (True)
- [tex]\(B\)[/tex] S1 floats in both L1 and L2. (False)
- [tex]\(C\)[/tex] S2 floats in both L1 and L2. (False)
- [tex]\(D\)[/tex] S2 floats in L1 but not in L2. (False)
Therefore, the correct answer is:
```
A: (True, False, False, False)
```
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