The gravitational force \( F \) 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,
- \( r \) is the distance between the centers of the two objects.
If we cut the mass of one of the objects (say \( m_1 \)) in half, the new mass \( m_1' \) will be:
\[ m_1' = \frac{m_1}{2} \]
Assuming the other mass \( m_2 \) and the distance \( r \) remain constant, the new gravitational force \( F' \) can be expressed as:
\[ F' = G \frac{m_1' m_2}{r^2} = G \frac{\left(\frac{m_1}{2}\right) m_2}{r^2} \]
Simplifying this, we have:
\[ F' = \frac{1}{2} \left(G \frac{m_1 m_2}{r^2}\right) = \frac{1}{2} F \]
This shows that if one of the object's masses is cut in half, the gravitational force between the two objects is also cut in half.
Therefore, the correct answer is:
a. The gravitational force is halved.