Question
If the mass of a planet is cut in half, how would the force of gravity between that planet and the Sun change?
The force of gravity would double
The force of gravity would not change
The force of gravity would increase four times
The force of gravity would decrease
The force of gravity would double
The force of gravity would not change
The force of gravity would increase four times
The force of gravity would decrease
Answers
GPT-4o mini
The gravitational force between two objects is described by Newton's law of universal gravitation, which states:
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the planet and the Sun),
- \( r \) is the distance between the centers of the two objects.
If the mass of the planet is cut in half, let's denote the original mass of the planet as \( m \). The new mass will be \( \frac{m}{2} \). The force of gravity between the planet and the Sun would then be calculated as:
\[ F' = G \frac{\left(\frac{m}{2}\right) m_{Sun}}{r^2} \]
This shows that the new gravitational force \( F' \) is half of the original gravitational force \( F \):
\[ F' = \frac{1}{2} \left( G \frac{m m_{Sun}}{r^2} \right) = \frac{1}{2} F \]
Therefore, the force of gravity between the planet and the Sun would decrease by half if the mass of the planet is cut in half.
So the correct answer is:
**The force of gravity would decrease.**
\[ F = G \frac{m_1 m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the planet and the Sun),
- \( r \) is the distance between the centers of the two objects.
If the mass of the planet is cut in half, let's denote the original mass of the planet as \( m \). The new mass will be \( \frac{m}{2} \). The force of gravity between the planet and the Sun would then be calculated as:
\[ F' = G \frac{\left(\frac{m}{2}\right) m_{Sun}}{r^2} \]
This shows that the new gravitational force \( F' \) is half of the original gravitational force \( F \):
\[ F' = \frac{1}{2} \left( G \frac{m m_{Sun}}{r^2} \right) = \frac{1}{2} F \]
Therefore, the force of gravity between the planet and the Sun would decrease by half if the mass of the planet is cut in half.
So the correct answer is:
**The force of gravity would decrease.**