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

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

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

1 answer

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:

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

If the mass of one object doubles (let's say \( m_1 \) becomes \( 2m_1 \)), the new gravitational force \( F' \) would be:

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

This indicates that the gravitational force will also double.

So, the correct response is:

The amount of the gravitational force doubles.