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)

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 doubles.
The gravitational force doubles.

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

The gravitational force decreases to one-fourth.

1 answer

The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the force \( F \) is proportional to the product of their masses \( m_1 \) 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 \( \frac{1}{2} m_1 \)), and the second object's mass (\( m_2 \)) remains the same, the new gravitational force \( F' \) would be:

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

This means the gravitational force decreases by one-half.

Therefore, the correct response is:

The gravitational force decreases by one-half.