Object A and Object B are at equal distances on opposite sides of Object C. Object B has three times the mass of Object C. Objects A and B have equal mass. What is the ratio of the gravitational force between Objects A and B to the gravitational force between Objects B and C? (1 point) Responses

A.3/4
B.3
C.2
D 3/2

D. 3/2

helo

FORTNITE BATTLE PASS

3

F = GMm/r^2

To find the ratio of the gravitational force between objects A and B to the gravitational force between objects B and C, we can use Newton's law of universal gravitation.

The formula for gravitational force is:

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

Let's assign some variables:
- mC = mass of Object C
- mA = mass of Object A
- mB = mass of Object B

Given that Object B has three times the mass of Object C, we can say:
mB = 3 * mC

Also, it is mentioned that Objects A and B have equal mass, so:
mA = mB

Now, let's calculate the gravitational force between objects A and B and the gravitational force between objects B and C:

ForceAB = G * (mA * mB) / r^2
ForceBC = G * (mB * mC) / r^2

Substituting the values of mB and mA:

ForceAB = G * (mA * 3 * mC) / r^2
ForceBC = G * (3 * mC * mC) / r^2

Simplifying:

ForceAB = G * 3 * (mA * mC) / r^2
ForceBC = G * 3 * (mC * mC) / r^2

Now, let's calculate the ratio of ForceAB to ForceBC:

Ratio = ForceAB / ForceBC

Substituting the values obtained above:

Ratio = (3 * (mA * mC) / r^2) / (3 * (mC * mC) / r^2)
Ratio = (mA * mC) / (mC * mC)

Since mA = mB and mB = 3 * mC:

Ratio = (mA * mC) / (mC * mC)
Ratio = (3 * mC * mC) / (mC * mC)
Ratio = 3

Therefore, the ratio of the gravitational force between Objects A and B to the gravitational force between Objects B and C is 3.

The correct answer is option B.