Choose the correct statement from the following :

Options

A. Elastic forces are always conservative.
B. Elastic forces are not always conservative.
C. Elastic force are conservative only when Hooke's is obeyed.
D. Elastic forces may be conservative even when Hooke's law is not obeyed.

Answer

To solve the question of identifying the correct statements regarding elastic forces, we will analyze the properties of elastic forces and Hooke's law step by step.

### Step 1: Understand Elastic Forces
Elastic forces are defined as the forces that attempt to restore a material to its original shape after deformation. These forces arise when a material is stretched or compressed.

**Hint:** Recall the definition of elastic forces and their role in restoring shape.

### Step 2: Determine if Elastic Forces are Conservative
A conservative force is one where the work done by the force on an object moving between two points is independent of the path taken. Elastic forces are generally considered conservative when they obey Hooke's law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position.

**Hint:** Think about the relationship between work done and path independence for conservative forces.

### Step 3: Analyze Hooke's Law
Hooke's law states that the force exerted by an elastic material is directly proportional to the amount of deformation (displacement) within the elastic limit. If a material obeys Hooke's law, it is typically considered to have conservative elastic forces.

**Hint:** Remember that Hooke's law applies only within certain limits of deformation.

### Step 4: Consider Non-Hookean Behavior
If a material does not obey Hooke's law, it may exhibit non-linear elastic behavior or plastic deformation. In these cases, the elastic forces may not be conservative, as the work done may depend on the path taken.

**Hint:** Reflect on the implications of materials that do not follow Hooke's law.

### Step 5: Evaluate the Statements
Now, we evaluate the statements given in the question:
1. Elastic forces are always conservative.
2. Elastic forces can be conservative if they obey Hooke's law.
3. Elastic forces are never conservative.
4. Elastic forces can be conservative even if they do not obey Hooke's law.

From our analysis:
- Statement 2 is correct: Elastic forces can be conservative if they obey Hooke's law.
- Statement 4 is also correct: Elastic forces can still be considered conservative under certain conditions, even if Hooke's law is not obeyed.

### Conclusion
The correct statements are:
- Option 2: Elastic forces can be conservative if they obey Hooke's law.
- Option 4: Elastic forces can be conservative even if they do not obey Hooke's law.

### Final Answer
The correct options are 2 and 4.

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