Of which of the following is g independent ?

Options

A. Mass of the earth
B. Size of the earth
C. Mass of an object thrown vertically upward or downward
D. All of these

Answer

To determine which of the following factors the acceleration due to gravity (g) is independent of, we can analyze the relationship of g with various parameters.

### Step-by-Step Solution:

1. **Understanding the Formula for g**:
The acceleration due to gravity (g) at the surface of the Earth is given by the formula:
\[ g = \frac{GM}{R^2} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

2. **Analyzing the Factors**:
- **Mass of the Earth (M)**: From the formula, we see that g is directly proportional to the mass of the Earth. Therefore, g depends on the mass of the Earth.
- **Size of the Earth (R)**: Similarly, g is inversely proportional to the square of the radius of the Earth. Thus, g also depends on the size of the Earth.
- **Mass of an Object**: The mass of an object thrown vertically (whether upward or downward) does not appear in the formula for g. This indicates that g is independent of the mass of the object.

3. **Conclusion**:
Based on the analysis, we conclude that the acceleration due to gravity (g) is independent of the mass of an object thrown vertically upward or downward.

### Final Answer:
g is independent of the mass of an object thrown vertically upward or downward.