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

The gravitational force doubles.
The gravitational force doubles.

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.

Answer 1

The correct response is:

The gravitational force decreases by one-half.

According to Newton's law of universal gravitation, the gravitational force (F) between two objects is given by the formula:

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

where \( m_1 \) and \( m_2 \) are the masses of the two objects, \( r \) is the distance between their centers, and \( G \) is the gravitational constant.

If the mass of one of the objects is halved (let's say \( m_1 \) becomes \( \frac{m_1}{2} \)), the new gravitational force will be:

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

This shows that the gravitational force decreases to one-half.