Question

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

Answer 1

To determine between which two objects the gravitational attraction is the greatest, we can use the formula for gravitational force:

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

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.

Since the distance \(r\) (1 meter) and the gravitational constant \(G\) are constant for all objects, the gravitational attraction will be greatest between the two objects with the largest product of their masses (\(m_1 \times m_2\)).

Let's calculate the products of the masses for the different pairs:

1. Small pot and book:

   • Masses: \(1,200\) g and \(860\) g
   • Product: \(1,200 \times 860 = 1,032,000\)

2. Penny and small pot:

   • Masses: \(2.5\) g and \(1,200\) g
   • Product: \(2.5 \times 1,200 = 3,000\)

3. Book and cereal box:

   • Masses: \(860\) g and \(500\) g
   • Product: \(860 \times 500 = 430,000\)

4. Paper clip and penny:

   • Masses: \(1.0\) g and \(2.5\) g
   • Product: \(1.0 \times 2.5 = 2.5\)

Now we can compare the results:

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

The greatest gravitational attraction is between the small pot and the book, with a product of \(1,032,000\).

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