Answer:
the correct answer is b) The gravitational force would increase by a factor of 2.
Step-by-step explanation:
To determine the effect of changing the distance and mass on the gravitational force between two masses, we can consider Newton's Law of Universal Gravitation. According to this law, the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Let's analyze each change separately:
1. Increasing the distance between the masses by a factor of 5:
- The gravitational force is inversely proportional to the square of the distance. Therefore, increasing the distance by a factor of 5 will result in the gravitational force decreasing by a factor of 5^2 = 25.
2. Increasing one of the masses by a factor of 50:
- The gravitational force is directly proportional to the product of the masses. Therefore, increasing one of the masses by a factor of 50 will result in the gravitational force increasing by a factor of 50.
Combining these two changes, the overall effect on the gravitational force can be calculated by multiplying the factors:
- The gravitational force decreases by a factor of 25 due to the increased distance.
- The gravitational force increases by a factor of 50 due to the increased mass.
Therefore, the net effect on the gravitational force is an increase of 50 / 25 = 2.
In conclusion, the gravitational force would increase by a factor of 2 if the distance between the masses was increased by a factor of 5 and one of the masses was increased by a factor of 50.
Therefore, the correct answer is b) The gravitational force would increase by a factor of 2.