There are two objects close to each other. If the mass of one of the objects is doubled while the distance remains the same, how does the gravitational force change?(1 point)

Question

Responses

It becomes four times stronger
It becomes four times stronger

It becomes half as strong
It becomes half as strong

It remains the same
It remains the same

It becomes twice as strong

Answer 1

According to the law of universal gravitation, the gravitational force \( F \) between two objects is given by the equation:

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

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

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

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

This means the gravitational force becomes twice as strong.

Therefore, the correct response is:

It becomes twice as strong.