To determine which image shows objects exerting less gravitational force on each other, we can use Newton's law of universal gravitation, which states that the gravitational force (F) between two objects is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers.
Let's analyze the two options:
- Option A: 10 billion kg and 1 billion kg
- Option B: 10 billion kg and 2 billion kg
In both cases, we can ignore the distance for this comparison as it is not provided, and we will assume it is the same for both pairs.
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For Option A:
- \( F_A \propto 10 \text{ billion kg} \times 1 \text{ billion kg} = 10 \times 1 = 10 \text{ billion kg}^2 \)
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For Option B:
- \( F_B \propto 10 \text{ billion kg} \times 2 \text{ billion kg} = 10 \times 2 = 20 \text{ billion kg}^2 \)
Since \( F_A \) (10 billion kg²) is less than \( F_B \) (20 billion kg²), the objects in Option A (10 billion kg and 1 billion kg) are exerting less gravitational force on each other than those in Option B (10 billion kg and 2 billion kg).
Therefore, objects in Image A are exerting less gravitational force on each other.