STATEMENT-1 : Tension at every point in a string with mass at every cross section must be unequal , if the string is accelerating .
and
STATEMENT - 2 : If we draw free body diagram for any section of the string , net external force acting on the string has to be equal to product of its mass ( which is non- zero ) and its acceleration .

Options

A. Statement -1 True, Statement -2 is True , Statement - 2 is a correct explanation for Statement -2
B. Statement -1 is True , Statement -2 is True , Statement -2 is NOT a correct explanation for statement -2
C. Statement -1 is true, Statement -2 is False
D. Statement - 1 is False , Statement - 2 is True

Answer

To solve the given problem, we need to analyze both statements and determine their validity based on the principles of physics, particularly Newton's laws of motion.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- Statement 1 claims that "Tension at every point in a string with mass at every cross section must be unequal if the string is accelerating."
- To evaluate this, we consider a string that is accelerating. If we take a small segment of the string, the tension at one end of the segment (let's call it T1) and the tension at the other end (T2) can be analyzed.

2. **Analyzing the Forces**:
- For a small element of the string with mass \( dm \), the net force acting on it can be expressed as:
\[ T1 - T2 = dm \cdot a \]
- Here, \( a \) is the acceleration of the string, and \( dm \) is the mass of the small segment.

3. **Conclusion for Statement 1**:
- From the equation \( T1 - T2 = dm \cdot a \), it is clear that if the string is accelerating, the tensions \( T1 \) and \( T2 \) must indeed be different (i.e., \( T1 \neq T2 \)). Therefore, Statement 1 is **true**.

4. **Understanding Statement 2**:
- Statement 2 states that "If we draw a free body diagram for any section of the string, the net external force acting on the string has to be equal to the product of its mass (which is non-zero) and its acceleration."
- This is a direct application of Newton’s second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

5. **Applying Newton's Second Law**:
- For the entire string, if we consider the total mass \( M \) and the acceleration \( a \), the net force \( F \) acting on the string can be expressed as:
\[ F = M \cdot a \]
- This is consistent with the free body diagram analysis where the net force is the difference in tension at the ends of the string.

6. **Conclusion for Statement 2**:
- Since the statement correctly reflects Newton's second law, Statement 2 is **true**.

### Final Evaluation:
- **Statement 1**: True (Tension must be unequal in an accelerating string).
- **Statement 2**: True (Net force equals mass times acceleration).