The acceleration due to gravity

Options

A. decreases on account of rotation of earth.
B. increases with increase in latitude of a place.
C. increases on account of rotation of earth.
D. increases in moving away from the centre if r gt radius of earth.

Answer

To solve the problem regarding the acceleration due to gravity and its variations, we will analyze the effects of Earth's rotation and latitude on gravitational acceleration.

### Step-by-Step Solution:

1. **Understanding Acceleration Due to Gravity (g)**:
The acceleration due to gravity at a point on the surface of the Earth is denoted by \( g \) and is given by the formula:
\[ g = \frac{GM}{R^2} \]
where \( G \) is the universal gravitational constant, \( M \) is the mass of the Earth, and \( R \) is the radius of the Earth.

**Hint**: Remember that \( g \) is influenced by both the mass of the Earth and the distance from its center.

2. **Effect of Earth's Rotation**:
When the Earth rotates, a centrifugal force acts on objects on its surface. This force reduces the effective gravitational force experienced by objects. The centrifugal force \( F_c \) can be expressed as:
\[ F_c = m \omega^2 r \]
where \( \omega \) is the angular velocity of the Earth and \( r \) is the distance from the axis of rotation.

**Hint**: Consider how the rotation of the Earth creates a force that opposes gravity.

3. **Components of Forces**:
At a latitude \( \theta \), the effective gravitational force \( g' \) can be expressed as:
\[ g' = g - F_c \cos(\theta) \]
Here, \( F_c \cos(\theta) \) is the component of the centrifugal force acting in the direction opposite to gravity.

**Hint**: Think about how the angle \( \theta \) affects the components of the forces acting on an object.

4. **Variation with Latitude**:
As latitude increases, \( \theta \) increases, which means \( \cos(\theta) \) decreases. This leads to a smaller centrifugal force component acting against gravity, thus increasing the effective gravitational acceleration \( g' \).

**Hint**: Remember that as you move towards the poles (increasing latitude), the effective gravitational force increases.

5. **Distance from the Center of the Earth**:
As you move away from the center of the Earth (i.e., increase \( R \)), the value of \( g \) decreases because \( g \) is inversely proportional to the square of the distance from the center of the Earth.

**Hint**: Consider how increasing the distance from the center of the Earth affects gravitational force.

6. **Conclusion**:
- The acceleration due to gravity decreases due to the rotation of the Earth.
- The acceleration due to gravity increases with an increase in latitude.
- The acceleration due to gravity decreases when moving away from the center of the Earth.

Therefore, the correct statements are:
- **Decreases on account of rotation of the Earth** (Correct)
- **Increases with increase in latitude** (Correct)

The incorrect statement is that it increases when moving away from the center of the Earth.

### Final Answer:
The correct options are:
- **A**: Decreases on account of rotation of Earth.
- **B**: Increases with increase in latitude of a place.