Statement-1: A gas filled balloon stops rising after it has attained a certain height in the sky.
Statement-2: At the highest point the density of air is such that the buoyant force on the balloon just equals its weight.

Options

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

Answer

To analyze the given statements, we will break down the concepts involved in buoyancy and the behavior of gases in a balloon.

### Step-by-Step Solution:

1. **Understanding the Balloon's Behavior**:
- A gas-filled balloon rises in the atmosphere because the gas inside the balloon (e.g., helium) is less dense than the surrounding air. This difference in density creates a buoyant force that acts upwards on the balloon.

2. **Buoyant Force**:
- The buoyant force is given by Archimedes' principle, which states that the upward buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the balloon displaces air.

3. **Rising to a Certain Height**:
- As the balloon rises, it encounters lower air pressure and density. The density of the air decreases with altitude. Eventually, the balloon will reach a height where the density of air becomes such that the buoyant force acting on the balloon equals the weight of the balloon itself.

4. **Equilibrium Condition**:
- At this point of equilibrium, the upward buoyant force is exactly balanced by the weight of the balloon. Therefore, the balloon stops rising. This condition is described by Statement-2.

5. **Conclusion**:
- Both statements are true:
- Statement-1 is true because the balloon does stop rising after reaching a certain height.
- Statement-2 is true because at that height, the buoyant force equals the weight of the balloon, which explains why it stops rising.

### Final Answer:
- Statement 1 is true.
- Statement 2 is true.
- Statement 2 is the correct explanation for Statement 1.