Two objects or 5kg to 10kg respectively and they're 10m apart. If the distance between them is increased to 20m, what happens to the gravitational force? A. it decreases B. it is doubled C. it increases slightly
it is doubled
To understand what happens to the gravitational force between two objects when the distance between them changes, we can use the universal law of gravitation. This law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Mathematically, the equation for gravitational force (F) between two objects is given by:
F = (G * m1 * m2) / (r^2)
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we have two different scenarios:
Scenario 1: The objects are 10m apart.
Scenario 2: The objects are 20m apart.
Let's calculate the gravitational force in both scenarios:
Scenario 1 (10m apart):
F1 = (G * m1 * m2) / (r^2)
F1 = (6.67430 × 10^-11 N m^2/kg^2) * (5kg * 10kg) / (10m^2)
F1 = (6.67430 × 10^-11 N m^2/kg^2) * 50kg / 100m^2
F1 = 3.33715 × 10^-12 N
Scenario 2 (20m apart):
F2 = (G * m1 * m2) / (r^2)
F2 = (6.67430 × 10^-11 N m^2/kg^2) * (5kg * 10kg) / (20m^2)
F2 = (6.67430 × 10^-11 N m^2/kg^2) * 50kg / 400m^2
F2 = 8.34288 × 10^-13 N
Comparing the forces, we can conclude that F2 (force when the objects are 20m apart) is smaller than F1 (force when the objects are 10m apart). Therefore, the gravitational force decreases when the distance between the objects is increased to 20m.
So, the correct answer is option A: It decreases.