The value of 'g' on earth surface depends :-

Options

A. only an earth's structure
B. only an earth's rotational motion
C. On above both
D. on none these and is same

Answer

To determine the factors on which the value of 'g' (acceleration due to gravity) on the Earth's surface depends, we can analyze the gravitational force and the relevant equations.

### Step-by-Step Solution:

1. **Understanding the Concept of Gravitational Force**:
The gravitational force between two masses is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between the centers of the two masses.

2. **Applying the Concept to Earth**:
For an object of mass \( m \) on the surface of the Earth, the gravitational force acting on it (which is also its weight) can be expressed as:
\[ F = m \cdot g \]
where \( g \) is the acceleration due to gravity at the Earth's surface.

3. **Relating 'g' to Earth's Mass and Radius**:
The gravitational force can also be expressed using the mass of the Earth \( M_e \) and the radius of the Earth \( R_e \):
\[ m \cdot g = \frac{G \cdot M_e \cdot m}{R_e^2} \]
By canceling \( m \) from both sides (assuming \( m \neq 0 \)), we get:
\[ g = \frac{G \cdot M_e}{R_e^2} \]

4. **Identifying the Dependencies**:
From the equation \( g = \frac{G \cdot M_e}{R_e^2} \), we can see that:
- \( g \) depends directly on the mass of the Earth \( M_e \) (as a larger mass leads to a stronger gravitational pull).
- \( g \) depends inversely on the square of the radius of the Earth \( R_e \) (as a larger radius leads to a weaker gravitational pull).

5. **Considering Earth's Rotation**:
The value of 'g' can also be affected by the rotation of the Earth. The centrifugal force due to Earth's rotation slightly reduces the effective value of 'g' experienced at the surface. Therefore, both the structure of the Earth (mass and radius) and its rotational motion influence the value of 'g'.

6. **Conclusion**:
Thus, the value of 'g' on the Earth's surface depends on:
- The Earth's structure (mass and radius).
- The rotational motion of the Earth.

### Final Answer:
The value of 'g' on the Earth's surface depends on both the Earth's structure and its rotational motion.