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**1. Homework Statement**

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. Homework 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?