On account of the earth rotating about its axis

Options

A. the linear velocity of objects at equator is greater than at other places.
B. the angular velocity of object at equator is more than that of object at poles.
C. the linear velocity of object at all places at the earth is equal, but angular velocity is different.
D. at all places the angular velocity and linear velocity are uniform.

Answer

To solve the question regarding the effects of the Earth's rotation about its axis, we will analyze the concepts of angular velocity and linear velocity at different points on the Earth's surface.

### Step-by-Step Solution:

1. **Understanding Angular Velocity**:
- The Earth rotates about its axis, and this rotation can be described by angular velocity (ω). Angular velocity is defined as the rate of change of angular displacement and is the same for all points on the Earth’s surface.
- **Conclusion**: The angular velocity of the Earth is constant and equal at all points on its surface, including the equator and the poles.

**Hint**: Remember that angular velocity is the same for all points on a rotating body.

2. **Understanding Linear Velocity**:
- Linear velocity (v) at any point on the Earth's surface depends on the radius (r) from the axis of rotation and is given by the formula:
\[ v = \omega \cdot r \]
- At the equator, the radius is maximum (equal to the radius of the Earth, R). As you move towards the poles, the effective radius decreases because the distance from the axis of rotation decreases.

**Hint**: Linear velocity varies with the distance from the axis of rotation.

3. **Calculating Linear Velocity at Different Points**:
- At the equator (θ = 0°), the radius is R, so:
\[ v_{equator} = \omega \cdot R \]
- At a latitude θ, the radius can be expressed as:
\[ r = R \cdot \cos(\theta) \]
- Thus, the linear velocity at latitude θ becomes:
\[ v_{\theta} = \omega \cdot (R \cdot \cos(\theta)) \]
- This shows that as θ increases (moving towards the poles), the linear velocity decreases.

**Hint**: Use the cosine function to determine how the radius changes with latitude.

4. **Comparing Linear Velocities**:
- Since \( \cos(\theta) \) decreases from 1 (at the equator) to 0 (at the poles), it follows that:
\[ v_{equator} > v_{\theta} \text{ (for any } \theta > 0\text{)} \]
- Therefore, the linear velocity at the equator is greater than at any other latitude.

**Hint**: Remember that linear velocity is maximum at the equator and decreases towards the poles.

5. **Evaluating the Options**:
- Based on the analysis:
- **Option A**: Linear velocity at the equator is greater than at other places - **True**.
- **Option B**: Angular velocity at the equator is more than at the poles - **False** (angular velocity is the same everywhere).
- **Option C**: Linear velocity of the object at all points of the Earth is equal - **False**.
- **Option D**: Angular velocity and linear velocity are uniform at all places - **False** (only angular velocity is uniform).

**Conclusion**: The only correct option is **A**.

### Final Answer:
The correct option is **A**: The linear velocity of the object at the equator is greater than at other places.