The distance between two particles of masses m₁ and m₂ is r. If the distances of these particles from the centre of mass of the system are r₁ and r₂ respectively, then show that
r₁ = r [ m₂ / (m₁ + m₂)]
r₂ = r [ m₁ / (m₁ + m₂)]
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According to Universal law of gravitation, the force of attraction between 2 bodies is:-
F = (G m1m2)/r2
Where m1m2 = the masses of the two bodies,
r = distance between them
G = gravitational Constant
When the distance is reduced to half i.e. r’ = (1/2) r then,
F’ = (G m1m2)/r2
= (G m1m2)/(r/2)2
= (4 G m1m2)/ (r2) = 4F
Therefore when the distance between the objects is reduced to half, then the force of gravitation increases by four times the original force.
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