To determine between which two objects the gravitational attraction is the greatest when placed 1 meter apart, we can use Newton's law of universal gravitation, which states that the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) is given by:
\[ F = G \frac{m_1 \times m_2}{r^2} \]
Where:
- \( G \) 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 masses.
Since \( G \) and \( r \) are constants for this particular scenario (1 meter apart), we can simply focus on the product of the masses \( m_1 \times m_2 \). The greater the product of the masses, the greater the gravitational attraction.
Let's calculate the products for each pair:
-
Paper clip (1.0 g) and penny (2.5 g):
\( 1.0 \times 2.5 = 2.5 \) -
Paper clip (1.0 g) and book (860 g):
\( 1.0 \times 860 = 860 \) -
Paper clip (1.0 g) and cereal box (500 g):
\( 1.0 \times 500 = 500 \) -
Paper clip (1.0 g) and small pot (1,200 g):
\( 1.0 \times 1200 = 1200 \) -
Penny (2.5 g) and book (860 g):
\( 2.5 \times 860 = 2150 \) -
Penny (2.5 g) and cereal box (500 g):
\( 2.5 \times 500 = 1250 \) -
Penny (2.5 g) and small pot (1,200 g):
\( 2.5 \times 1200 = 3000 \) -
Book (860 g) and cereal box (500 g):
\( 860 \times 500 = 430000 \) -
Book (860 g) and small pot (1,200 g):
\( 860 \times 1200 = 1032000 \) -
Cereal box (500 g) and small pot (1,200 g):
\( 500 \times 1200 = 600000 \)
Now, let's identify the pairs with the largest products:
- Between the book and the small pot: 1032000 (highest)
Thus, the gravitational attraction is greatest between the book and the small pot.