The mass of an object decreases by one-half. What happens to the gravitational force between the object and a second object whose mass stays the same?(1 point)

Question

Responses

The gravitational force decreases by one-half.
The gravitational force decreases by one-half.

The gravitational force stays the same, as long as the objects remain on Earth.
The gravitational force stays the same, as long as the objects remain on Earth.

The gravitational force decreases to one-fourth.
The gravitational force decreases to one-fourth.

The gravitational force doubles.

Answer 1

The gravitational force between two objects is described by Newton's Law of Universal Gravitation, which is given by the formula:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

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 masses.

If the mass of one object decreases by one-half (\( m_1 \) becomes \( \frac{m_1}{2} \)), while the mass of the second object (\( m_2 \)) remains the same, the new gravitational force (\( F' \)) becomes:

\[ F' = \frac{G \cdot \frac{m_1}{2} \cdot m_2}{r^2} \]

This can be simplified to:

\[ F' = \frac{1}{2} \cdot \left( \frac{G \cdot m_1 \cdot m_2}{r^2} \right) = \frac{1}{2} F \]

Therefore, the gravitational force decreases by one-half.

Thus, the correct response is:

The gravitational force decreases by one-half.