To determine which two objects have the greatest gravitational attraction when placed 1 meter apart, we can use the formula for gravitational force:
\[ F = G \frac{m_1 m_2}{r^2} \]
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 the objects (which is constant at 1 meter for our comparison).
Since \( G \) and \( r^2 \) are constant in this scenario, we can simplify the comparison to just the product of the masses \( m_1 \) and \( m_2 \).
Let's calculate the products of the masses for each pair of objects:
-
Paper clip (1.0 g) and Penny (2.5 g): \[ 1.0 \times 2.5 = 2.5 \]
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Penny (2.5 g) and Small pot (1,200 g): \[ 2.5 \times 1,200 = 3,000 \]
-
Book (860 g) and Cereal box (500 g): \[ 860 \times 500 = 430,000 \]
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Small pot (1,200 g) and Book (860 g): \[ 1,200 \times 860 = 1,032,000 \]
Now, let's compare these products:
- Between paper clip and penny: \( 2.5 \)
- Between penny and small pot: \( 3,000 \)
- Between book and cereal box: \( 430,000 \)
- Between small pot and book: \( 1,032,000 \)
Thus, the greatest gravitational attraction occurs between the small pot and the book.