Two spherical bubbles sit side by side in a (effectively infinite) sea of fluid

Question

Two spherical bubbles sit side by side in a (effectively infinite) sea of fluid of density p= 1.2 kg/m3. They are 4.0 cm apart and each has a radius of 0.5 cm. Also, assume that they contain no mass. Assume no other gravitational fields are in effect.

A) Derive the force of bubble 2 on bubble 1

b) Consider now that a spherical bubble of the same size but containing a fluid with density 2p replacing bubble 1. Find the magnitude and direction of the force on bubble 1 now.

--This question is worded correctly but I cannot figure how the evacuated bubbles can exert a gravitational force on one another, but I know it has something to do with them submerged in the liquid... please help!

Explanation / Answer

try this hint: imagine the bubbles are made of negative mass and density equal in magnitude to the density of the "normal" fluid, by superimposing a hypothetical negative mass over normal mass, we can create, at least mathematically, a region of zero mass now find the gravitational attraction between these two negative mass spheres: F = G (-m1)(-m2)/(0.04m)^2 m1 = density x volume of the sphere, so calculate these masses in kg in the second case, you have one sphere of twice as much normal mass and only one sphere made of this hypothetical negative mass...notice the signs of the masses now...what is the direction of the force?

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