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 paper clip and the penny
between the paper clip and the penny
between the penny and the small pot
Answers
GPT-4o mini
To determine between which two objects the gravitational attraction is the greatest when placed 1 meter apart, we can use the formula for gravitational attraction:
\[ F = G \frac{m_1 \cdot m_2}{d^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (which is the same for all pairs),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( d \) is the distance between the objects (1 meter in this case).
Since \( G \) and \( d \) are constant for our comparisons, we can simply look at the product of the masses \( m_1 \cdot m_2 \) of each pair to determine which pair will have the greatest gravitational attraction.
Let's calculate the products of the masses for each pair.
1. **Small pot (1200 g) and book (860 g)**:
\( 1200 \times 860 = 1,032,000 \)
2. **Book (860 g) and cereal box (500 g)**:
\( 860 \times 500 = 430,000 \)
3. **Paper clip (1 g) and penny (2.5 g)**:
\( 1 \times 2.5 = 2.5 \)
4. **Penny (2.5 g) and small pot (1200 g)**:
\( 2.5 \times 1200 = 3000 \)
Now, comparing these products:
- **Small pot and book**: 1,032,000
- **Book and cereal box**: 430,000
- **Paper clip and penny**: 2.5
- **Penny and small pot**: 3000
The greatest product is \( 1,032,000 \) between the **small pot and the book**.
Therefore, the answer is:
**between the small pot and the book**.
\[ F = G \frac{m_1 \cdot m_2}{d^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (which is the same for all pairs),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( d \) is the distance between the objects (1 meter in this case).
Since \( G \) and \( d \) are constant for our comparisons, we can simply look at the product of the masses \( m_1 \cdot m_2 \) of each pair to determine which pair will have the greatest gravitational attraction.
Let's calculate the products of the masses for each pair.
1. **Small pot (1200 g) and book (860 g)**:
\( 1200 \times 860 = 1,032,000 \)
2. **Book (860 g) and cereal box (500 g)**:
\( 860 \times 500 = 430,000 \)
3. **Paper clip (1 g) and penny (2.5 g)**:
\( 1 \times 2.5 = 2.5 \)
4. **Penny (2.5 g) and small pot (1200 g)**:
\( 2.5 \times 1200 = 3000 \)
Now, comparing these products:
- **Small pot and book**: 1,032,000
- **Book and cereal box**: 430,000
- **Paper clip and penny**: 2.5
- **Penny and small pot**: 3000
The greatest product is \( 1,032,000 \) between the **small pot and the book**.
Therefore, the answer is:
**between the small pot and the book**.