Minimum period of rotation and gravity

[Tonyt88]

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?

Homework Equations

T = 2 pi r
...v

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

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?

 

[neutrino]

How does dr/dT relate to this problem?

Read the question carefully, and try to use the "givens." In this case, you are required to find the minimum of period of rotation, which is given as a function of the velcocity.

Your substitution was right. Note that the planet's density is also provided. Remember that density = mass.volume

 

[Tonyt88]

Hmmm, so am I not supposed to find a derivative somewhere, or?