Force of gravitational attraction is least -

Options

A. at the equator
B. at the poles
C. at a point in between equator and any pole
D. none of the above.

Answer

To determine where the force of gravitational attraction is least, we can analyze the gravitational force at different locations on Earth: at the equator, at the poles, and at points in between.

### Step-by-Step Solution:

1. **Understanding Gravitational Force**:
The gravitational force acting on an object of mass \( m \) is given by the equation:
\[ F = m \cdot g \]
where \( g \) is the acceleration due to gravity.

2. **Acceleration due to Gravity at Different Locations**:
The value of \( g \) varies depending on the location on Earth:
- At the **poles**, \( g \) is maximum because there is no centrifugal force acting on the object (the radius of the circular path is zero).
- At the **equator**, \( g \) is affected by the centrifugal force due to the Earth's rotation, which reduces the effective gravitational force. The effective gravitational force at the equator can be expressed as:
\[ g_{\text{equator}} = g - \omega^2 r_e \]
where \( \omega \) is the angular velocity of the Earth's rotation and \( r_e \) is the radius of the Earth at the equator.

3. **Gravitational Force at the Midpoint**:
At any point between the equator and the poles, the effective gravitational force can be calculated by considering both the gravitational force and the centrifugal force. The effective gravitational force can be expressed as:
\[ g = \sqrt{g^2 + (\omega^2 r)^2 - 2g(\omega^2 r) \cos(\theta)} \]
where \( \theta \) is the angle from the vertical.

4. **Comparing Values of \( g \)**:
- Since \( g \) is maximum at the poles and minimum at the equator, we conclude that:
- \( g_{\text{pole}} > g_{\text{midpoint}} > g_{\text{equator}} \)

5. **Conclusion**:
The force of gravitational attraction is least at the equator because the centrifugal force reduces the effective gravitational force more than at any other point on Earth. Therefore, the correct answer is:
\[ \text{The force of gravitational attraction is least at the equator.} \]