To determine between which two objects gravitational attraction is the greatest, we must use the formula for gravitational force, which is given by Newton's law of universal gravitation:
\[ F = G \frac{{m_1 m_2}}{{r^2}} \]
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 centers of the two objects (in this case, 1 meter).
Since the distance is constant (1 meter), we focus on maximizing the product of the masses \(m_1 m_2\).
Let's calculate the products of the masses for each pair of objects:
-
Paper clip (1.0 g) and Penny (2.5 g): \[ 1.0 \times 2.5 = 2.5 \]
-
Penny (2.5 g) and Small Pot (1,200 g): \[ 2.5 \times 1200 = 3000 \]
-
Small Pot (1,200 g) and Book (860 g): \[ 1200 \times 860 = 1,032,000 \]
-
Book (860 g) and Cereal Box (500 g): \[ 860 \times 500 = 430,000 \]
Now, let's compare these values:
- Paper clip and Penny: 2.5
- Penny and Small Pot: 3000
- Small Pot and Book: 1,032,000
- Book and Cereal Box: 430,000
The greatest product of masses is between the Small Pot and the Book (1,032,000).
Therefore, the gravitational attraction is greatest between the small pot and the book.