# Two small balls, A and B, attract each other gravitationally

Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one

F’ = F

Hence, the magnitude of the attractive force remains same.

Explanation:

The force of attraction between two bodies is given by Newton’s Gravitational Law:

F = Gm₁m₂/r² ————— equation 1

where,

F = Force of attraction between balls

G = Universal Gravitational Constant

m₁ = mass of first ball

m₂ = mass of 2nd ball

r = distance between balls

Now, we double the masses of both balls and the separation between them. So, the force of attraction becomes:

F’ = Gm₁’m₂’/r’²

here,

m₁’ = 2 m₁

m₂’ = 2 m₂

r’ = 2 r

Therefore,

F’ = G(2 m₁)(2 m₂)/(2 r)²

F’ = Gm₁m₂/r²

using equation 1:

F’ = F

Hence, the magnitude of the attractive force remains same.

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