The value of acceleration due to gravity on earth depends on

Options

A. mass of the body
B. radius of the body
C. shape of the body
D. mass of the earth

Explanation

To determine the factors on which the acceleration due to gravity (g) on Earth depends, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Concept of Gravity:**
The acceleration due to gravity at the surface of the Earth is a result of the gravitational force exerted by the Earth on an object. This force depends on the mass of the Earth and the distance from its center.

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

3. **Analyzing the Factors:**
- **Mass of the Body (Option 1):** The formula shows that the mass of the object (small m) does not appear in the equation for g. Therefore, the acceleration due to gravity does not depend on the mass of the body.
- **Radius of the Body (Option 2):** The radius of the body also does not affect the value of g. The formula only considers the radius of the Earth.
- **Shape of the Body (Option 3):** The shape of the body does not influence the acceleration due to gravity. The gravitational force acts uniformly on all objects regardless of their shape.
- **Mass of the Earth (Option 4):** The mass of the Earth is a crucial factor in determining the value of g, as seen in the formula.

4. **Conclusion:**
From the analysis, we can conclude that the acceleration due to gravity on Earth primarily depends on:
- The mass of the Earth (M_e)
- The radius of the Earth (R_e)

Thus, the correct answer is that the acceleration due to gravity depends on the mass of the Earth and the radius of the Earth.

### Final Answer:
The value of acceleration due to gravity on Earth depends on the mass of the Earth and the radius of the Earth.