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

between the book and the cereal box
between the book and the cereal box

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

between the paper clip and the penny

1 answer

To determine between which two objects the gravitational attraction is greatest when placed 1 meter apart, we can use Newton's law of universal gravitation. The gravitational force (\(F\)) between two objects is determined by the equation:

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

where:

  • \(F\) is the gravitational force,
  • \(G\) is the gravitational constant,
  • \(m_1\) and \(m_2\) are the masses of the two objects, and
  • \(r\) is the distance between their centers (in this case, 1 meter).

The force is directly proportional to the product of the two masses, so we want to find the pair of objects with the highest product of their masses.

Let's analyze the pairs based on the masses given:

  1. Between the small pot (1,200 g) and the book (860 g):

    • Product: \(1,200 \cdot 860 = 1,032,000\)
  2. Between the book (860 g) and the cereal box (500 g):

    • Product: \(860 \cdot 500 = 430,000\)
  3. Between the penny (2.5 g) and the small pot (1,200 g):

    • Product: \(2.5 \cdot 1,200 = 3,000\)
  4. Between the paper clip (1.0 g) and the penny (2.5 g):

    • Product: \(1.0 \cdot 2.5 = 2.5\)

Now, comparing these products, we find:

  • Small pot and book: 1,032,000
  • Book and cereal box: 430,000
  • Penny and small pot: 3,000
  • Paper clip and penny: 2.5

The greatest product of masses is between the small pot and the book.

Therefore, the correct answer is:

between the small pot and the book.