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.