To solve the problem, we need to analyze the information given about the diglyceride and the fatty acid it produces upon hydrolysis.
### Step-by-Step Solution:
1. **Understanding the Hydrolysis of Diglycerides**:
- A diglyceride (or diglycerol) is a glycerol molecule bonded to two fatty acid molecules. Upon hydrolysis, it breaks down into glycerol and fatty acids.
- The problem states that hydrolysis of the diglyceride yields glycerol and a single fatty acid.
2. **Identifying the Fatty Acid**:
- The formula of the fatty acid given is \( C_{15}H_{31}COOH \).
- This structure indicates that it is a long-chain fatty acid, specifically a saturated fatty acid known as palmitic acid, which has the common name derived from its 16 carbon atoms (including the carboxylic acid group).
3. **Determining the Type of Lipid**:
- Since the hydrolysis yields glycerol and only one type of fatty acid, we can conclude that the diglyceride is a simple lipid. Simple lipids consist of glycerol and fatty acids.
4. **Identifying the Specific Diglyceride**:
- The options provided are:
- (A) Simple lipid
- (B) 1, 2-stearin
- (C) 1, 2-palmitin
- (D) 1, 3-palmitin
- Since we know that the fatty acid produced is palmitic acid, we need to determine which of the diglycerides listed contains palmitic acid.
- The terms "1, 2-stearin" and "1, 3-palmitin" suggest that they contain stearic acid and palmitic acid, respectively.
5. **Conclusion**:
- The diglyceride that would yield palmitic acid upon hydrolysis is either 1, 2-palmitin or 1, 3-palmitin.
- Therefore, the correct answer is that the diglyceride is a simple lipid that can be represented as either 1, 2-palmitin or 1, 3-palmitin, but since the question asks for a specific diglyceride, we can conclude that both options C and D are correct.
### Final Answer:
The diglyceride is **(A) Simple lipid** and can also be **(C) 1, 2-palmitin** or **(D) 1, 3-palmitin**.
