STATEMENT - 1 : A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle `theta` without changing its speed. The impulse imparted to the ball is zero.
because
STATEMENT - 2 : Impulse = change in momentum.

Options

A. Statement - 1 is 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 the two statements provided and determine their validity based on the principles of physics, particularly the concepts of impulse and momentum.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A ball of mass \( m \) is moving towards a batsman with a speed \( v \).
- The batsman strikes the ball, deflecting it at an angle \( \theta \) without changing its speed.

2. **Defining Impulse**:
- Impulse is defined as the change in momentum of an object when a force is applied over a period of time.
- Mathematically, impulse \( J \) can be expressed as:
\[ J = \Delta p = p_{\text{final}} - p_{\text{initial}} \]
- Where \( p \) is momentum, given by \( p = mv \).

3. **Calculating Initial Momentum**:
- The initial momentum of the ball before the batsman strikes it is:
\[ p_{\text{initial}} = mv \]

4. **Calculating Final Momentum**:
- After being struck, the ball continues to move with the same speed \( v \) but in a different direction (deflected by angle \( \theta \)).
- The final momentum can be expressed as:
\[ p_{\text{final}} = mv' \quad \text{(where \( v' = v \) since speed is unchanged)} \]
- The direction of the momentum changes, but the magnitude remains the same.

5. **Change in Momentum**:
- Since the speed remains the same but the direction changes, we need to consider the vector nature of momentum.
- The change in momentum can be calculated as:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} \]
- Since the ball's direction changes, the momentum before and after the strike is not the same, leading to a non-zero change in momentum.

6. **Conclusion on Impulse**:
- Since there is a change in momentum, the impulse imparted to the ball is not zero.
- Therefore, **Statement 1** is false.

7. **Validity of Statement 2**:
- Statement 2 correctly states that impulse is equal to the change in momentum, which is a fundamental principle in physics. Thus, **Statement 2** is true.

### Final Conclusion:
- **Statement 1** is false, and **Statement 2** is true.