Question
According to the law of universal gravitation, the force of gravity between two objects is proportional to the masses of the objects and:
Directly proportional to the cube of the distance between them
Inversely proportional to the square of the distance between them
Inversely proportional to the cube of the distance between them
Directly proportional to the square of the square of the distance between them
Directly proportional to the cube of the distance between them
Inversely proportional to the square of the distance between them
Inversely proportional to the cube of the distance between them
Directly proportional to the square of the square of the distance between them
Answers
GPT-4o mini
According to the law of universal gravitation, the force of gravity between two objects is **inversely proportional to the square of the distance between them**.
This means that as the distance between the two objects increases, the gravitational force decreases by the square of that distance. Mathematically, this is represented by the equation:
\[ F = G \frac{m_1 m_2}{r^2} \]
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 the centers of the two objects.
This means that as the distance between the two objects increases, the gravitational force decreases by the square of that distance. Mathematically, this is represented by the equation:
\[ F = G \frac{m_1 m_2}{r^2} \]
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 the centers of the two objects.