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 effects of the acceleration due to gravity on a brass ball when it is brought to a planet where the gravitational acceleration is one-fourth that of Earth. Let's go through the solution step by step.

### Step 1: Understand the given information
- The acceleration due to gravity on the surface of the planet (let's call it \( g' \)) is one-fourth of that on Earth (denoted as \( g \)).
- Therefore, we can express this relationship mathematically as:
\[ g' = \frac{g}{4} \]

### Step 2: Analyze the mass of the brass ball
- The mass of an object is defined as the amount of matter it contains and is independent of the gravitational field.
- Therefore, when the brass ball is brought to the planet, its mass remains unchanged.
- Let the mass of the brass ball be \( m \). Thus, the mass on Earth and the mass on the planet is:
\[ m_{\text{Earth}} = m_{\text{planet}} = m \]

### Step 3: Calculate the weight of the brass ball on Earth
- The weight of an object is given by the formula:
\[ W = m \cdot g \]
- On Earth, the weight of the brass ball is:
\[ W_{\text{Earth}} = m \cdot g \]

### Step 4: Calculate the weight of the brass ball on the planet
- Using the modified gravitational acceleration on the planet, the weight of the brass ball on the planet can be calculated as:
\[ W_{\text{planet}} = m \cdot g' = m \cdot \left(\frac{g}{4}\right) = \frac{m \cdot g}{4} \]
- This shows that the weight of the brass ball on the planet is one-fourth of its weight on Earth.

### Step 5: Conclusion
- The mass of the brass ball remains constant, while its weight decreases to one-fourth of its weight on Earth.
- Therefore, the correct answer is that the mass remains the same, and the weight becomes one-fourth.

### Final Answer
- Mass remains constant.
- Weight becomes one-fourth.