Question
If the mass of a planet is cut in half, how would the force of gravity between that planet and the Sun change?(1 point)
Responses
The force of gravity would double
The force of gravity would double
The force of gravity would not change
The force of gravity would not change
The force of gravity would increase four times
The force of gravity would increase four times
The force of gravity would decrease
Responses
The force of gravity would double
The force of gravity would double
The force of gravity would not change
The force of gravity would not change
The force of gravity would increase four times
The force of gravity would increase four times
The force of gravity would decrease
Answers
GPT-4o mini
The force of gravity between two objects is described by Newton's law of universal gravitation, which states that the gravitational force \( F \) is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers. The formula is given by:
\[
F = G \frac{m_1 m_2}{r^2}
\]
where:
- \( F \) is the force of gravity,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects, and
- \( r \) is the distance between their centers.
If the mass of the planet is cut in half (\( m_1/2 \)), the equation for the force of gravity becomes:
\[
F' = G \frac{\left(\frac{m_1}{2}\right) m_2}{r^2} = \frac{1}{2} \left(G \frac{m_1 m_2}{r^2}\right) = \frac{1}{2} F
\]
Thus, the new gravitational force \( F' \) would be half of the original force \( F \).
Based on this understanding, the correct response is:
**The force of gravity would decrease.**
\[
F = G \frac{m_1 m_2}{r^2}
\]
where:
- \( F \) is the force of gravity,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects, and
- \( r \) is the distance between their centers.
If the mass of the planet is cut in half (\( m_1/2 \)), the equation for the force of gravity becomes:
\[
F' = G \frac{\left(\frac{m_1}{2}\right) m_2}{r^2} = \frac{1}{2} \left(G \frac{m_1 m_2}{r^2}\right) = \frac{1}{2} F
\]
Thus, the new gravitational force \( F' \) would be half of the original force \( F \).
Based on this understanding, the correct response is:
**The force of gravity would decrease.**