Final answer:
When the mass of each sphere is doubled, the gravitational force between them becomes four times greater, resulting in a new force of (d) 4000 N.
Step-by-step explanation:
The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the force (F) is proportional to the product of the two masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers.
The formula for gravitational force is F = G * (m1 * m2) / r2, where G is the gravitational constant.
If we double the mass of each of the two metal spheres, the new force (Fnew) would be Fnew = G * (2m1 * 2m2) / r2 = 4 * G * (m1 * m2) / r2 = 4 * (original force), assuming the distance between them remains the same. Therefore, if the original force is 1000 N, the new force would be 4 * 1000 N = 4000 N.