Answer:
5 times smaller
Step-by-step explanation:
To calculate the new gravitational force, we use Newton's law of universal gravitation, which states that the attraction force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In this scenario, the distance between the two galaxies has increased by a factor of 5, so the new gravitational force will be:
F = G(m1*m2)/(r^2)
Where G is the gravitational constant, m1 and m2 are the masses of the galaxies, and r is the distance between the centers of the galaxies. Since the new distance is 5 times farther than the original distance, we can use the formula for proportion to find the new gravitational force:
F2 = F1*k
Where F2 is the new gravitational force, F1 is the original gravitational force, and k is the change in distance. Substitute the expression for the gravitational force and the given values, and we get:
F2 = G(m1m2)/(r^2) = G(m1m2)/(5r)^2
Simplifying the expression, we get:
F2 = (1/5)^2*F1
So the new gravitational force is 5 times smaller than the original force. The correct answer is b. 25 times smaller.