To determine which scenario will experience a stronger gravitational force, we need to refer to Newton's Law of Gravitation. Newton's Law of Gravitation states that every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between two objects,
- [tex]\( G \)[/tex] is the gravitational constant,
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects,
- [tex]\( r \)[/tex] is the distance between the centers of the two masses.
Let's evaluate the given scenarios based on the information provided.
### Scenario A:
The objects have equal masses, each with mass [tex]\( M \)[/tex].
Here, the gravitational force can be calculated as:
[tex]\[ F_A = G \frac{M \cdot M}{r^2} = G \frac{M^2}{r^2} \][/tex]
### Scenario B:
The object on the left has a mass of [tex]\( 2M \)[/tex] and the object on the right has a mass [tex]\( M \)[/tex].
Here, the gravitational force can be calculated as:
[tex]\[ F_B = G \frac{2M \cdot M}{r^2} = G \frac{2M^2}{r^2} \][/tex]
### Comparison:
To determine which scenario has a stronger gravitational force, we compare [tex]\( F_A \)[/tex] and [tex]\( F_B \)[/tex]:
- [tex]\( F_A = G \frac{M^2}{r^2} \)[/tex]
- [tex]\( F_B = G \frac{2M^2}{r^2} \)[/tex]
Clearly, [tex]\( F_B \)[/tex] is twice [tex]\( F_A \)[/tex]:
[tex]\[ F_B = 2 \times F_A \][/tex]
### Conclusion:
The object on the left with a mass of [tex]\( 2M \)[/tex] (Scenario B) will experience a stronger gravitational force compared to the scenario where both objects have equal masses [tex]\( M \)[/tex] (Scenario A). Therefore, the correct answer is:
The object on the left has a mass of [tex]\( 2M \)[/tex] (Scenario B) will experience a stronger gravitational force.
