Two bodies of the same mass, located at some distance from each other, are attracted with force What will be the force of attraction F2 if, without changing the distance between the bodies, half the mass of the first body is transferred to the second?
The force of attraction between two bodies is determined by the formula:
F = G * m1 * m2 / R ^ 2, where
G – gravitational constant, m1, m2 – body masses, R – distance between bodies.
According to the condition of the problem, in the first case, the force of attraction will be equal to:
F1 = G * m1 * m2 / R ^ 2 = G * m ^ 2 / R ^ 2 (since the masses of both bodies are the same).
According to the condition of the problem, half of the mass of the first body was transferred to the second, that is:
m1 = m / 2, m2 = m + m / 2 = 3 * m / 2.
Then, in the second case, the force of attraction will be equal to:
F2 = G * m1 * m2 / R ^ 2 = G * m ^ 2 * 3 / (4 * R ^ 2).
Dividing F1 by F2 we get:
F1 / F2 = G * m ^ 2 * 4 * R ^ 2 / (R ^ 2 * G * m ^ 2 * 3) = 4/3, that is:
F2 = 3 * F1 / 4
Answer: F2’s gravity will decrease by 1/4 of F1.