The gravitational force between 1 kg of lead and Earth is _________ the gravitational force between 1 kg of melon and earth-------- ?

Options

A. greater than
B. the same as
C. less than
D. none of the above

Answer

To solve the question, we need to understand the concept of gravitational force as described by the law of gravitation. The gravitational force between two objects depends on their masses and the distance between them.

### Step-by-Step Solution:

1. **Understanding Gravitational Force**:
The gravitational force (F) between two objects can be calculated using the formula:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( G \) is the universal gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers.

2. **Identify the Masses**:
- For the first part (lead and Earth):
- \( m_1 \) (mass of lead) = 1 kg
- \( m_2 \) (mass of Earth) = \( 6 \times 10^{24} \) kg
- For the second part (melon and Earth):
- \( m_1 \) (mass of melon) = 1 kg
- \( m_2 \) (mass of Earth) = \( 6 \times 10^{24} \) kg

3. **Calculate Gravitational Force for Lead**:
Using the formula:
\[ F_{lead} = \frac{G \cdot 1 \cdot 6 \times 10^{24}}{r^2} \]

4. **Calculate Gravitational Force for Melon**:
Similarly, for the melon:
\[ F_{melon} = \frac{G \cdot 1 \cdot 6 \times 10^{24}}{r^2} \]

5. **Comparison of Forces**:
- Since both gravitational forces depend on the same formula and the same values of \( m_2 \) (mass of Earth) and \( r \) (distance), we can conclude that:
\[ F_{lead} = F_{melon} \]

6. **Final Answer**:
Therefore, the gravitational force between 1 kg of lead and Earth is **equal to** the gravitational force between 1 kg of melon and Earth.

### Conclusion:
The gravitational force between 1 kg of lead and Earth is **equal to** the gravitational force between 1 kg of melon and Earth.

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