To determine between which two objects the gravitational attraction is greatest, we can use Newton's law of universal gravitation, which states that the gravitational force \( F \) between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between them.
Since the distance is constant (1 meter) for the comparisons, we can focus on the product of the masses \( m_1 \times m_2 \) to find the greatest gravitational attraction.
Now, let's calculate \( m_1 \times m_2 \) for each pair of objects:
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Between the book (860g) and the cereal box (500g): \[ 860 \times 500 = 430,000 \]
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Between the penny (2.5g) and the small pot (1,200g): \[ 2.5 \times 1,200 = 3,000 \]
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Between the paper clip (1.0g) and the penny (2.5g): \[ 1.0 \times 2.5 = 2.5 \]
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Between the small pot (1,200g) and the book (860g): \[ 1,200 \times 860 = 1,032,000 \]
Now we compare the products:
- Between the book and the cereal box: 430,000
- Between the penny and the small pot: 3,000
- Between the paper clip and the penny: 2.5
- Between the small pot and the book: 1,032,000 (greatest)
The greatest gravitational attraction is between the small pot and the book.
So the correct response is:
between the small pot and the book.
1 answer