Question

In: Physics

Suppose two worlds, each having mass M and radius R, coalesce into a single world. Due...

Suppose two worlds, each having mass M and radius R, coalesce into a single world. Due to gravitational contraction, the combined world has a radius of only 7/8 R. What is the average density of the combined world as a multiple of ρ0, the average density of the original two worlds?

Expert Solution

We know that density is given by:

Density = Mass/Volume

Given that:

0 = average density of original two worlds = M/V = M/(4*pi*R^3/3) = 3M/(4*pi*R^3)

Suppose density of combined world = , then

= Combined mass of both worlds/Volume of new world

Combined mass of both worlds = M + M = 2M

Volume of new world = V1 = (4/3)*pi*R1^3

Given that R1 = (7/8)*R, So

= 2M/((4/3)*pi*R1^3) = 6M/(4*pi*R1^3)

dividing both equations

/0 = [6M/(4*pi*R1^3)]/[3M/(4*pi*R^3)]

/0 = 2*(R/R1)^3

/0 = 2*(R/(7/8)*R)^3 = 2*(8/7)^3

/0 = 2.985

= 2.985*0

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genius_generous answered 2 years ago

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