Question

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 1

Answer:

Drop by a factor of 64

Explanation:

By Newtons law of gravity,

$F=\frac{Gm₁m₂}{r^{2} }$ where;

G = Universal gravitaional constant

r = distance between center of gravities of two objects

m₁,m₂ = masses of thee objects.

F = Gravitational force.

m = $\frac{4}{3}π r³ρ$  (mass = volume into density.

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

m' = $\frac{4}{3}π (r/2)³ρ$

     = $\frac{1}{6}π r³ρ$

So in substitution to the equation,

$F'=\frac{G(m₁/8)(m₂/8)}{r^{2} }$

$F' = F/64$