The acceleration due to gravity on the surface of a planet is one - fourth of the value on Earth. When a brass ball is brought to this planet , its

Options

A. Mass is halved
B. Weight is halved
C. Mass becomes one - fourth
D. Weight becomes one - fourth

Answer

To solve the problem, we need to analyze the relationship between mass, weight, and acceleration due to gravity.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- Let \( g \) be the acceleration due to gravity on Earth.
- The acceleration due to gravity on the planet is given as \( g' = \frac{g}{4} \).

2. **Mass of the Brass Ball**:
- The mass \( m \) of the brass ball remains constant regardless of the location.
- Therefore, the mass of the brass ball on Earth and on the planet is the same: \( m \).

3. **Weight Calculation**:
- The weight \( W \) of an object is calculated using the formula:
\[ W = mg \]
- On Earth, the weight of the brass ball is:
\[ W_{Earth} = mg \]
- On the planet, the weight \( W' \) will be:
\[ W' = mg' = m \left(\frac{g}{4}\right) = \frac{mg}{4} \]
- This shows that the weight of the brass ball on the planet is one-fourth of its weight on Earth.

4. **Conclusion**:
- The mass of the brass ball remains the same.
- The weight of the brass ball on the planet is one-fourth of its weight on Earth.

### Final Answer:
- Mass remains the same.
- Weight becomes \( \frac{1}{4} \) of its weight on Earth.