Final answer:
When the masses of two particles are doubled and the distance between them is also doubled, the force of attraction between them remains the same according to Newton's Law of Universal Gravitation.
Step-by-step explanation:
If the mass of each of two particles is doubled and the distance between them is doubled, the force of attraction between the two particles would decrease. According to Newton's Law of Universal Gravitation, the force of attraction (F) between two masses is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers. The force can be represented by the equation F = G * (m1*m2) / r2, where G is the gravitational constant.
When both masses are doubled, the force would initially seem to increase by a factor of four (since 2m1 * 2m2 = 4m1 * m2). However, when the distance is also doubled, the denominator of the equation (r2) becomes 4 times larger because (2r)2 = 4 * r2. This means that the force is reduced by a factor of four, counteracting the initial increase due to the doubling of mass. Consequently, the net effect is that the force of attraction remains the same.