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)

Question

Responses

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

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

The amount of the gravitational force doubles.

Answer 1

The amount of the gravitational force doubles.

According to Newton's law of universal gravitation, the gravitational force \( F \) between two objects is directly 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. The formula is:

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

Where \( G \) is the gravitational constant. If the mass of one object doubles (let's say it changes from \( m_1 \) to \( 2m_1 \)), while the other mass \( m_2 \) and the distance \( r \) remain unchanged, the new gravitational force becomes:

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

So, the gravitational force doubles.