The mass of an object doubles. What happens to the gravitational force between it and another object whose mass stays the same, assuming they remain the same distance apart?(1 point)

Responses

The amount of the gravitational force decreases by one-half.
The amount of the gravitational force decreases by one-half.

The amount of the gravitational force quadruples.
The amount of the gravitational force quadruples.

The amount of the gravitational force remains the same.
The amount of the gravitational force remains the same.

The amount of the gravitational force doubles.
The amount of the gravitational force doubles.

1 answer

The amount of the gravitational force doubles.

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 object doubles (let's say \( m_1 \) becomes \( 2m_1 \)), and the other mass \( m_2 \) and the distance \( r \) remain the same, the new gravitational force can be calculated as follows:

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

Thus, the gravitational force doubles.