To solve the problem, we will analyze each statement (S1, S2, S3, S4) one by one and determine their validity based on the principles of physics.
### Step 1: Analyze Statement S1
**Statement:** If the internal forces within a system are conservative, then the work done by the external forces on the system is equal to the change in mechanical energy of the system.
**Analysis:**
- Internal forces being conservative means they do not dissipate energy. Instead, they store energy.
- The work-energy theorem states that the work done by external forces on a system is equal to the change in mechanical energy of that system.
- Therefore, this statement is **True**.
### Step 2: Analyze Statement S2
**Statement:** The potential energy of a particle moving along the x-axis in a conservative force field is \( U = 2x^2 - 5x + 1 \). It has a stable equilibrium position at one point on the x-axis.
**Analysis:**
- To find the equilibrium position, we need to find the minimum of the potential energy function \( U \).
- We differentiate \( U \) with respect to \( x \) and set the derivative to zero:
\[
\frac{dU}{dx} = 4x - 5 = 0 \implies x = \frac{5}{4}
\]
- To confirm that this is a minimum, we can check the second derivative:
\[
\frac{d^2U}{dx^2} = 4 > 0
\]
- Since the second derivative is positive, \( x = \frac{5}{4} \) is indeed a point of stable equilibrium.
- Thus, this statement is **True**.
### Step 3: Analyze Statement S3
**Statement:** Internal forces can perform net work on a rigid body.
**Analysis:**
- In a rigid body, the distances between any two points remain constant regardless of the forces applied.
- If internal forces act on a rigid body, they will do equal and opposite work on different parts of the body, resulting in a net work of zero.
- Therefore, this statement is **False**.
### Step 4: Analyze Statement S4
**Statement:** Internal forces can perform net work on a non-rigid body.
**Analysis:**
- In a non-rigid body, the distances between points can change. Therefore, internal forces can indeed perform net work as they can cause deformation and movement of parts of the body without being countered by equal and opposite forces.
- Thus, this statement is **True**.
### Conclusion
Based on the analysis:
- S1: True
- S2: True
- S3: False
- S4: True
Therefore, the overall answer is TDFT (True, True, False, True).
