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 penny and the small pot
between the penny and the small pot

between the small pot and the book
between the small pot and the book

between the book and the cereal box

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 objects is directly proportional to the product of their masses \( m_1 \) and \( m_2 \) and inversely proportional to the square of the distance \( r \) between them:

\[ F = G \frac{m_1 m_2}{r^2} \]

Since the distance is constant (1 meter in this case), we can compare the products of the masses of the objects.

Let's calculate the mass products for each pair of objects:

  1. Paper clip and penny: \( 1.0 \times 2.5 = 2.5 \) grams²
  2. Penny and small pot: \( 2.5 \times 1200 = 3000 \) grams²
  3. Small pot and book: \( 1200 \times 860 = 1,032,000 \) grams²
  4. Book and cereal box: \( 860 \times 500 = 430,000 \) grams²

Now, let's compare the products:

  • Paper clip and penny: 2.5 grams²
  • Penny and small pot: 3000 grams²
  • Small pot and book: 1,032,000 grams²
  • Book and cereal box: 430,000 grams²

The greatest gravitational attraction, therefore, is between the small pot and the book (1,032,000 grams²).

So the answer is: between the small pot and the book.