A person weighs 98 N at the surface of earth. Its mass at the centre of earth will be

Options

A. Zero
B. 1 kg
C. 0.1 kg
D. 10 kg

Answer

To find the mass of a person who weighs 98 N at the surface of the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between weight and mass**:
The weight (W) of an object is given by the formula:
\[ W = m \cdot g \]
where:
- \( W \) is the weight,
- \( m \) is the mass,
- \( g \) is the acceleration due to gravity.

2. **Identify the known values**:
From the problem, we know:
- Weight \( W = 98 \, \text{N} \)
- Acceleration due to gravity at the surface of the Earth \( g \approx 9.8 \, \text{m/s}^2 \).

3. **Rearrange the formula to solve for mass**:
We can rearrange the weight formula to find the mass:
\[ m = \frac{W}{g} \]

4. **Substitute the known values into the equation**:
\[ m = \frac{98 \, \text{N}}{9.8 \, \text{m/s}^2} \]

5. **Calculate the mass**:
\[ m = 10 \, \text{kg} \]

6. **Conclusion about mass at the center of the Earth**:
The mass of an object remains constant regardless of its position (whether at the surface or at the center of the Earth). Therefore, the mass of the person at the center of the Earth is also:
\[ \text{Mass} = 10 \, \text{kg} \]

### Final Answer:
The mass of the person at the center of the Earth is **10 kg**.

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