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.**