Final answer:
The gravitational force between two masses will be doubled if the distance between them is increased by a factor of five, and one of the masses is increased by a factor of 50, according to Newton's Law of Universal Gravitation.
Step-by-step explanation:
To understand what happens to gravitational force between two masses when one mass is multiplied by 50 and the distance is increased by a factor of 5, we need to apply Newton's Law of Universal Gravitation. This law states that the gravitational force (F) between two masses (m1 and m2) is proportional to the product of their masses and inversely proportional to the square of the distance (r) between them:
F = G * (m1 * m2) / r^2
When the distance is increased by a factor of 5, the new force F' will be:
F' = G * (m1 * (50 * m2)) / (5r)^2 = G * (50 * m1 * m2) / (25 * r^2)
Thus, the new force can be found by dividing the original force by 25 and then multiplying by 50:
F' = (50/25) * F = 2 * F
So, the gravitational force will be doubled.