STATEMENT-1 : Acceleration of a particle in a reference frame may be non- zero , even if net external force acting on the particle is zero.
and
STATEMENT : 2 In a non- - inertial reference frame, Newton's second law is not valid.

Options

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

Answer

To solve the problem, we need to analyze both statements and their relationship to each other.

### Step-by-Step Solution:

**Step 1: Understanding Statement 1**
- Statement 1 claims that the acceleration of a particle in a reference frame may be non-zero, even if the net external force acting on the particle is zero.
- This can happen in a non-inertial reference frame. For example, if a block is at rest on the surface of the Earth, the forces acting on it (gravity and normal force) are balanced, resulting in zero net force. However, if we observe this block from a non-inertial frame (like a car accelerating), the observer would see the block accelerating backward relative to them.

**Step 2: Understanding Statement 2**
- Statement 2 asserts that in a non-inertial reference frame, Newton's second law is not valid.
- This is true because Newton's laws are formulated for inertial frames, where objects either remain at rest or move at constant velocity unless acted upon by a net external force. In non-inertial frames, fictitious forces must be considered to apply Newton's laws correctly.

**Step 3: Relationship Between the Statements**
- Since Statement 1 is true (acceleration can be non-zero in a non-inertial frame despite zero net external force), and Statement 2 correctly explains why this occurs (Newton's second law does not hold in non-inertial frames), we conclude that both statements are true and that Statement 2 is a correct explanation for Statement 1.

### Final Conclusion:
- Both Statement 1 and Statement 2 are true, and Statement 2 provides a correct explanation for Statement 1. Therefore, the correct answer is option A.