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23. Two spheres, with radii of R, are in contact with each other and attract each other with a force of F. If the radii of both of the spheres are cut to half while the density remains the same, what is the new gravitational force between them?

Answer :

Hania12

Answer:

Drop by a factor of 64

Explanation:

By Newtons law of gravity,

[tex]F=\frac{Gm₁m₂}{r^{2} }[/tex] where;

G = Universal gravitaional constant

r = distance between center of gravities of two objects

m₁,m₂ = masses of thee objects.

F = Gravitational force.

m = [tex]\frac{4}{3}π r³ρ[/tex]  (mass = volume into density.

So when radius is halved, mass drops by a factor of 8,

m' = [tex]\frac{4}{3}π (r/2)³ρ[/tex]

     = [tex]\frac{1}{6}π r³ρ[/tex]

So in substitution to the equation,

[tex]F'=\frac{G(m₁/8)(m₂/8)}{r^{2} }[/tex]

[tex]F' = F/64[/tex]

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