At the surface of a certain planet acceleration due to gravity is one - quarter of that on earth If a brass ball is transported to this planet , then which one of the following statements is not correct ? .

Options

A. The mass of the brass ball on this planet is a quarter
B. The weight of the brass ball on this planet is a quarter of the weight as measured on earth.
C. The brass ball has the same mass on the other planet as on earth
D. The brass ball has the same volume on the other planet as on earth

Explanation

To solve the problem, we need to analyze the statements given about a brass ball transported to a planet where the acceleration due to gravity is one-quarter of that on Earth. We will evaluate each statement to determine which one is not correct.

### Step-by-Step Solution

1. **Understanding Acceleration Due to Gravity**:
- On Earth, the acceleration due to gravity (g) is approximately 9.8 m/s².
- On the given planet, the acceleration due to gravity (g') is one-quarter of that on Earth:
\[ g' = \frac{g}{4} = \frac{9.8}{4} \approx 2.45 \, \text{m/s}^2 \]

2. **Analyzing Each Statement**:
- **Statement A**: "The mass of the brass ball on this planet is a quarter of its mass as measured on Earth."
- **Analysis**: Mass is a measure of the amount of matter in an object and does not change regardless of location. Therefore, this statement is **incorrect**.

- **Statement B**: "The weight of the brass ball on this planet is a quarter of the weight as measured on Earth."
- **Analysis**: Weight is given by the formula \( W = mg \). On Earth, the weight is \( W = mg \). On the new planet, the weight will be:
\[ W' = m \cdot g' = m \cdot \left(\frac{g}{4}\right) = \frac{mg}{4} \]
This means the weight on the new planet is one-quarter of the weight on Earth. Thus, this statement is **correct**.

- **Statement C**: "The brass ball has the same mass on the other planet as on Earth."
- **Analysis**: As previously mentioned, mass remains constant regardless of location. Therefore, this statement is **correct**.

- **Statement D**: "The brass ball has the same volume on the other planet as on Earth."
- **Analysis**: Volume is determined by the mass and density of the material. Since the mass remains constant and the material (brass) does not change, the volume will also remain the same. Thus, this statement is **correct**.

3. **Conclusion**:
- The only statement that is not correct is **Statement A**: "The mass of the brass ball on this planet is a quarter of its mass as measured on Earth."

### Final Answer:
The incorrect statement is **Statement A**.

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