Dimensional analysis to estimate gas clounds collapse

[leonne]

Homework Statement

stars form by gravitational collapse of interstellar gas clouds. use dimensional analysis to estimate how long it takes for a cloud with a density p=Mo pc^-3 to collapse

Mo= 1.9898e33 g

Homework Equations

The Attempt at a Solution

I just have no idea how to use dimensional analysis, and how I would use it to solve the problem. My book has nothing about it. So if someone can explain to me how I use dimensional analysis step by step solve this problem.

Thanks

 

[leonne]

Hey
after reading I have better idea on what to do. Here is what i got.

PgML/po I have to try to get the signs to cancle out and just to be left with time right?

so P= ML^-3 for density g= M^-1 L³ T^-2 for gravity. po = MLT^-1 for momentum so all of the cancel and you are left with time. Is that the right formula? Hmmm but how am i suppose to find how long it will take without the mass length or momentum? or did i do something wrong?