Use the table of the masses of several objects to answer the question. Object Mass (grams) paper clip 1.0 penny 2.5 book 860 cereal box 500 small pot 1,200 Between which two objects is gravitational attraction the greatest if placed 1 meter apart? (1 point) Responses between the paper clip and the penny between the paper clip and the penny between the book and the cereal box between the book and the cereal box between the small pot and the book between the small pot and the book between the penny and the small pot..

1 answer

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:

  1. Paper clip (1.0 g) and penny (2.5 g):
    \( 1.0 \times 2.5 = 2.5 \)

  2. Paper clip (1.0 g) and book (860 g):
    \( 1.0 \times 860 = 860 \)

  3. Paper clip (1.0 g) and cereal box (500 g):
    \( 1.0 \times 500 = 500 \)

  4. Paper clip (1.0 g) and small pot (1,200 g):
    \( 1.0 \times 1200 = 1200 \)

  5. Penny (2.5 g) and book (860 g):
    \( 2.5 \times 860 = 2150 \)

  6. Penny (2.5 g) and cereal box (500 g):
    \( 2.5 \times 500 = 1250 \)

  7. Penny (2.5 g) and small pot (1,200 g):
    \( 2.5 \times 1200 = 3000 \)

  8. Book (860 g) and cereal box (500 g):
    \( 860 \times 500 = 430000 \)

  9. Book (860 g) and small pot (1,200 g):
    \( 860 \times 1200 = 1032000 \)

  10. 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.