The gravitational force \( F \) between two masses is given by Newton's law of universal gravitation:

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

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

Originally, \( F = 10 \, \text{N} \).

If both masses are doubled (\( m_1' = 2P \), \( m_2' = 2Q \)) and \( r \) remains constant, the new force is:

\(F' = G \frac{(2P)(2Q)}{r^2} = G \frac{4PQ}{r^2} = 4 \left( G \frac{PQ}{r^2} \right) = 4 \times 10 = 40 \, \text{N}\)