Consider a one dimensional head on collision of two balls.
Statement-1 : The loss in kinetic energy of the system during the collision does not depend on the velocity of the observer.
Statement-2 : Kinetic energy of a body is independent of velocity of observer.

Options

A. Statement-1 is true, Statement-2 is true and statement-2 is correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the problem, we need to analyze both statements regarding the head-on collision of two balls and their implications on kinetic energy and observer velocity.

### Step 1: Understanding Statement 1
**Statement 1:** The loss in kinetic energy of the system during the collision does not depend on the velocity of the observer.

In a collision, the kinetic energy before and after the collision can be calculated using the velocities of the objects involved. The loss in kinetic energy is determined by the initial and final velocities of the objects, which are invariant under a change of inertial reference frame (i.e., they remain the same regardless of the observer's velocity). Therefore, the loss in kinetic energy is indeed independent of the observer's velocity.

### Step 2: Understanding Statement 2
**Statement 2:** Kinetic energy of a body is independent of the velocity of the observer.

This statement is misleading. The kinetic energy of a body does depend on the observer's frame of reference. Kinetic energy is given by the formula \( KE = \frac{1}{2} mv^2 \). If the observer is moving, the velocity \( v \) of the body will appear different, and thus the kinetic energy will also appear different. Therefore, this statement is false.

### Step 3: Conclusion
- **Statement 1** is **True**: The loss in kinetic energy during the collision does not depend on the velocity of the observer.
- **Statement 2** is **False**: Kinetic energy of a body does depend on the velocity of the observer.

### Final Answer
The correct option is that **Statement 1 is true and Statement 2 is false**.

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