STATEMENT-1: Two balls are dropped one after the other form a tall tower. The distance between them increases linearly with time (elapsed after the second ball is dropped and before the first hits ground).
STATEMENT-2: Relative acceleration is zero, whereas relative velocity non-zero in the above situation.

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true.

Explanation

To solve the problem, we will analyze the two statements given and derive the necessary conclusions step by step.

### Step 1: Understanding the Problem
We have two balls dropped from a tall tower, one after the other. We need to analyze the distance between the two balls after the second ball is dropped and before the first ball hits the ground.

### Step 2: Analyzing the Motion of the Balls
- Let the first ball be dropped at time \( t = 0 \).
- The second ball is dropped at time \( t = t_0 \) (let's say after a short interval).
- The first ball will have fallen a distance \( h_1 = \frac{1}{2} g t^2 \) after time \( t \).
- The second ball, dropped at \( t_0 \), will fall a distance \( h_2 = \frac{1}{2} g (t - t_0)^2 \) after the same time \( t \).

### Step 3: Finding the Distance Between the Balls
The distance \( y \) between the two balls at time \( t \) after the second ball is dropped can be expressed as:
\[ y = h_1 - h_2 \]
Substituting the expressions for \( h_1 \) and \( h_2 \):
\[ y = \frac{1}{2} g t^2 - \frac{1}{2} g (t - t_0)^2 \]
Expanding \( (t - t_0)^2 \):
\[ y = \frac{1}{2} g t^2 - \frac{1}{2} g (t^2 - 2tt_0 + t_0^2) \]
Simplifying:
\[ y = \frac{1}{2} g (2tt_0 - t_0^2) \]
This shows that the distance \( y \) depends linearly on time \( t \) (since \( t \) is the variable).

### Step 4: Analyzing Relative Velocity and Acceleration
- The acceleration of both balls is \( g \) (downward).
- The relative acceleration between the two balls is:
\[ a_{rel} = a_1 - a_2 = g - g = 0 \]
- The relative velocity between the two balls can be calculated as:
\[ v_{rel} = v_1 - v_2 \]
Since both balls are accelerating downward, the relative velocity is non-zero.

### Conclusion
- **Statement 1**: The distance between the two balls increases linearly with time. **True.**
- **Statement 2**: The relative acceleration is zero, while the relative velocity is non-zero. **True.**
- Therefore, both statements are true, and Statement 2 correctly explains Statement 1.

### Final Answer
Both statements are true, and Statement 2 is the correct explanation for Statement 1.

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