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

The gravitational force doubles.

Answer 1

The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the gravitational force \( F \) is proportional to the product of the masses of the two objects \( m_1 \) and \( m_2 \), and inversely proportional to the square of the distance \( r \) between their centers:

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

If the mass of one object decreases by one-half (let's say \( m_1 \) becomes \( \frac{1}{2} m_1 \)) while the mass of the second object \( m_2 \) remains the same, the new gravitational force \( F' \) can be expressed as:

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

Thus, the gravitational force decreases by one-half.

The correct response is:

The gravitational force decreases by one-half.