(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a planet with uniform mass density p. If the planet rotates too fast, it will fly apart. Show that the minimum period of rotation is given by:

T = (3 pi)^(1/2)

......(G p)^(1/2)

What is the minimum T if p = 5.5 g/cm^3?

2. Relevant equations

T = 2 pi r

........v

v = (G m)^(1/2)

........(r)^(1/2)

3. The attempt at a solution

I combined the two equations to have:

T = 2 pi (r)^(3/2)

.......(G m)^(1/2)

I found dr/dT to have:

3 pi (r)^(1/2)

(G m)^(1/2)

What am I doing incorrectly?

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# Minimum period of rotation and gravity

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