To determine between which two objects the gravitational attraction is the greatest, we use the formula for gravitational force:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between the centers of the two objects (which is 1 meter in this case).
Since \( G \) and \( r^2 \) are constants for our comparisons, we can focus on the product of the masses \( m_1 \cdot m_2 \) for each pair of objects.
Calculating the products of the masses of each pair:
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Paper clip and penny: \[ 1.0 , \text{g} \times 2.5 , \text{g} = 2.5 , \text{g}^2 \]
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Penny and small pot: \[ 2.5 , \text{g} \times 1,200 , \text{g} = 3,000 , \text{g}^2 \]
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Book and cereal box: \[ 860 , \text{g} \times 500 , \text{g} = 430,000 , \text{g}^2 \]
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Small pot and book: \[ 1,200 , \text{g} \times 860 , \text{g} = 1,032,000 , \text{g}^2 \]
Now, we compare these values:
- Paper clip and penny: \( 2.5 , \text{g}^2 \)
- Penny and small pot: \( 3,000 , \text{g}^2 \)
- Book and cereal box: \( 430,000 , \text{g}^2 \)
- Small pot and book: \( 1,032,000 , \text{g}^2 \)
The greatest product is between the small pot and the book, which has a product of 1,032,000 g².
Thus, the answer is:
between the small pot and the book.