Use the table of the masses of several objects to answer the question.

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 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
between the paper clip and the penny

between the small pot and the book
between the small pot and the book
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GPT-4o mini · Answer

To determine between which two objects the gravitational attraction is greatest, 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 and inversely proportional to the square of the distance between their centers. The formula is:

$F = G \frac{m_{1} m_{2}}{r^{2}}$

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 them.

Since the distance is constant (1 meter) for the comparisons, we can focus on the product of the masses $m_{1} \times m_{2}$ to find the greatest gravitational attraction.

Now, let's calculate $m_{1} \times m_{2}$ for each pair of objects:

Between the book (860g) and the cereal box (500g): $860 \times 500 = 430, 000$
Between the penny (2.5g) and the small pot (1,200g): $2.5 \times 1, 200 = 3, 000$
Between the paper clip (1.0g) and the penny (2.5g): $1.0 \times 2.5 = 2.5$
Between the small pot (1,200g) and the book (860g): $1, 200 \times 860 = 1, 032, 000$

Now we compare the products:

Between the book and the cereal box: 430,000
Between the penny and the small pot: 3,000
Between the paper clip and the penny: 2.5
Between the small pot and the book: 1,032,000 (greatest)

The greatest gravitational attraction is between the small pot and the book.

So the correct response is:

between the small pot and the book.