How will the force of the gravitational interaction between two bodies change if the mass of the first body is halved
November 18, 2020 | education
| How will the force of the gravitational interaction between two bodies change if the mass of the first body is halved and the mass of the second body is doubled?
F = G * m1 * m2 / R², where G is the gravitational constant, m1 is the mass of the first body, m2 is the mass of the second body, R is the distance between the bodies.
The force of attraction before changing the masses of bodies:
F1 = G * m1,1 * m2,1 / R1².
The force of attraction after changing the masses of bodies:
F2 = G * m1.2 * m2.2 / R2².
m1.2 = 0.5m1.1; m2,2 = 2m2,1
F2 / F1 = (G * m1.1 * m2.1 / R2²) / (G * m1.2 * m2.2 / R1²) = m1.1 * m2.1 / (0.5m1.1 * 2m2.1 ) = 1 / (0.5 * 2) = 1/1 = 1.
Answer: a) The force of gravitational interaction will not change.
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