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?
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?
Answers
GPT-4o mini
To determine which two objects have the greatest gravitational attraction when placed 1 meter apart, 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 objects,
- \( r \) is the distance between the centers of the two masses.
Since \( G \) and \( r \) are constant for the purpose of this comparison, we can focus on the product \( m_1 m_2 \).
Let's evaluate the products of the masses of the objects given in grams:
1. **Paper clip (1.0 g) and penny (2.5 g)**:
\[ 1.0 \times 2.5 = 2.5 \]
2. **Paper clip (1.0 g) and book (860 g)**:
\[ 1.0 \times 860 = 860 \]
3. **Paper clip (1.0 g) and cereal box (500 g)**:
\[ 1.0 \times 500 = 500 \]
4. **Paper clip (1.0 g) and small pot (1,200 g)**:
\[ 1.0 \times 1200 = 1200 \]
5. **Penny (2.5 g) and book (860 g)**:
\[ 2.5 \times 860 = 2150 \]
6. **Penny (2.5 g) and cereal box (500 g)**:
\[ 2.5 \times 500 = 1250 \]
7. **Penny (2.5 g) and small pot (1,200 g)**:
\[ 2.5 \times 1200 = 3000 \]
8. **Book (860 g) and cereal box (500 g)**:
\[ 860 \times 500 = 430000 \]
9. **Book (860 g) and small pot (1,200 g)**:
\[ 860 \times 1200 = 1032000 \]
10. **Cereal box (500 g) and small pot (1,200 g)**:
\[ 500 \times 1200 = 600000 \]
Now, we compare all the products:
- \( 2.5, 860, 500, 1200, 2150, 1250, 3000, 430000, 1032000, 600000 \)
The highest product is \( 1032000 \), which comes from the **book (860 g)** and the **small pot (1,200 g)**.
Therefore, the greatest gravitational attraction occurs between the **book and the small pot** when placed 1 meter apart.
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the objects,
- \( r \) is the distance between the centers of the two masses.
Since \( G \) and \( r \) are constant for the purpose of this comparison, we can focus on the product \( m_1 m_2 \).
Let's evaluate the products of the masses of the objects given in grams:
1. **Paper clip (1.0 g) and penny (2.5 g)**:
\[ 1.0 \times 2.5 = 2.5 \]
2. **Paper clip (1.0 g) and book (860 g)**:
\[ 1.0 \times 860 = 860 \]
3. **Paper clip (1.0 g) and cereal box (500 g)**:
\[ 1.0 \times 500 = 500 \]
4. **Paper clip (1.0 g) and small pot (1,200 g)**:
\[ 1.0 \times 1200 = 1200 \]
5. **Penny (2.5 g) and book (860 g)**:
\[ 2.5 \times 860 = 2150 \]
6. **Penny (2.5 g) and cereal box (500 g)**:
\[ 2.5 \times 500 = 1250 \]
7. **Penny (2.5 g) and small pot (1,200 g)**:
\[ 2.5 \times 1200 = 3000 \]
8. **Book (860 g) and cereal box (500 g)**:
\[ 860 \times 500 = 430000 \]
9. **Book (860 g) and small pot (1,200 g)**:
\[ 860 \times 1200 = 1032000 \]
10. **Cereal box (500 g) and small pot (1,200 g)**:
\[ 500 \times 1200 = 600000 \]
Now, we compare all the products:
- \( 2.5, 860, 500, 1200, 2150, 1250, 3000, 430000, 1032000, 600000 \)
The highest product is \( 1032000 \), which comes from the **book (860 g)** and the **small pot (1,200 g)**.
Therefore, the greatest gravitational attraction occurs between the **book and the small pot** when placed 1 meter apart.