A ball floats on the surface of water in a container exposed to atmosphere.
Statement-1 : If the container is shifted to moon, the ball will rise a little (gravity on moon is `(1)/(6)`th that on the earth).
And
Statement-2 : Buoyant force on the ball will decrease.

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 both statements regarding the behavior of a floating ball when the container is moved from Earth to the Moon.

### Step-by-step Solution:

1. **Understanding the Floating Condition**:
- A ball floats in a liquid when the buoyant force acting on it is equal to its weight. This can be expressed as:
\[ F_b = mg \]
- Here, \( F_b \) is the buoyant force, \( m \) is the mass of the ball, and \( g \) is the acceleration due to gravity.

2. **Buoyant Force Calculation**:
- The buoyant force can also be expressed in terms of the density of the liquid (\( \rho \)), the volume of the displaced liquid (\( V \)), and the acceleration due to gravity (\( g \)):
\[ F_b = \rho V g \]
- For the ball to float, we have:
\[ \rho V g = mg \]
- This implies that the volume of the ball submerged in the liquid is such that the weight of the displaced liquid equals the weight of the ball.

3. **Effect of Moving to the Moon**:
- On the Moon, the acceleration due to gravity is \( \frac{1}{6} \)th that of Earth. Therefore, if the container is moved to the Moon, the weight of the ball will decrease:
\[ mg_{moon} = m \left(\frac{g}{6}\right) = \frac{mg}{6} \]
- The buoyant force will also be affected by the change in gravity:
\[ F_{b, moon} = \rho V \left(\frac{g}{6}\right) = \frac{\rho V g}{6} \]

4. **Analyzing Statement 1**:
- Statement 1 claims that the ball will rise a little on the Moon.
- Since both the weight of the ball and the buoyant force decrease by the same factor of \( \frac{1}{6} \), the condition for floating remains unchanged. Thus, the ball will not rise or sink; it will remain at the same level.
- **Conclusion**: Statement 1 is **false**.

5. **Analyzing Statement 2**:
- Statement 2 claims that the buoyant force on the ball will decrease.
- As calculated, the buoyant force on the Moon is indeed \( \frac{1}{6} \)th of what it is on Earth. Therefore, the buoyant force decreases.
- **Conclusion**: Statement 2 is **true**.

6. **Final Conclusion**:
- Since Statement 1 is false and Statement 2 is true, the correct answer is that Statement 1 is false and Statement 2 is true.

### Final Answer:
- Statement 1: False
- Statement 2: True