A body is weighed at the poles and then at the equator .The weight

Options

A. at the equator will be greater than at the poles
B. at the poles will be greater than at the equator
C. at the poles will be equal to the weight at the equator
D. depends upon the shape of the object

Explanation

To solve the problem of comparing the weight of a body at the poles and at the equator, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Weight and Gravity**:
The weight of a body is given by the formula:
\[ W = m \cdot g \]
where \( W \) is the weight, \( m \) is the mass of the body, and \( g \) is the acceleration due to gravity.

2. **Acceleration due to Gravity**:
The acceleration due to gravity \( g \) is defined as:
\[ g = \frac{G \cdot M}{r^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the distance from the center of the Earth to the object.

3. **Comparing Radii at Poles and Equator**:
The Earth is not a perfect sphere; it is slightly flattened at the poles and bulging at the equator. Therefore, the radius at the equator \( R_e \) is greater than the radius at the poles \( R_p \):
\[ R_e > R_p \]

4. **Effect on Gravity**:
Since \( g \) is inversely proportional to the square of the radius \( r \):
\[ g \propto \frac{1}{r^2} \]
This means that as \( r \) increases, \( g \) decreases. Therefore:
\[ g_e < g_p \]
where \( g_e \) is the acceleration due to gravity at the equator and \( g_p \) is the acceleration due to gravity at the poles.

5. **Calculating Weight at Poles and Equator**:
- Weight at the poles:
\[ W_p = m \cdot g_p \]
- Weight at the equator:
\[ W_e = m \cdot g_e \]

6. **Comparing Weights**:
Since \( g_p > g_e \), it follows that:
\[ W_p > W_e \]
This means the weight of the body at the poles is greater than its weight at the equator.

7. **Conclusion**:
Therefore, the correct answer is that the weight of the body at the poles is greater than at the equator.

### Final Answer:
The weight of the body at the poles is greater than at the equator.

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