When a body is taken from the equator to the poles, its weight

Options

A. remains same
B. increases
C. decreases
D. increases at N-pole and decreases at S-pole

Answer

To solve the question of how a body's weight changes when taken from the equator to the poles, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Weight**:
Weight (W) is defined as the force exerted on a body due to gravity. It can be calculated using the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity at that location.

2. **Identify the Variation of Gravity**:
The acceleration due to gravity \( g \) varies with location on the Earth's surface. It is influenced by two main factors:
- The distance from the center of the Earth (which varies from the equator to the poles due to the Earth's shape).
- The centrifugal force due to the Earth's rotation, which is greater at the equator.

3. **Compare the Radius at the Equator and the Poles**:
- The Earth is not a perfect sphere; it is an oblate spheroid. This means that the radius at the equator (let's denote it as \( r_1 \)) is greater than the radius at the poles (denote it as \( r_2 \)).
- Thus, \( r_1 > r_2 \).

4. **Acceleration due to Gravity at Different Locations**:
The formula for acceleration due to gravity is:
\[ g = \frac{GM}{r^2} \]
where \( G \) is the gravitational constant and \( M \) is the mass of the Earth. Since \( r \) is larger at the equator, \( g \) will be smaller at the equator compared to the poles.

5. **Conclusion on Weight Change**:
Since the acceleration due to gravity is greater at the poles than at the equator, the weight of the body will also be greater at the poles. Therefore, we can conclude that:
\[ W_{\text{pole}} > W_{\text{equator}} \]

### Final Answer:
The weight of the body increases when taken from the equator to the poles.