Estimate time scale of expansion of a star

[Poirot]

Homework Statement

A star experiences a sudden increase in pressure to a new value P'. Taking the average density as ρ and the radius R, estimate the time scale of expansion of the star. (Ignore gravity altogether).

Homework Equations

The only thing I can see in my notes that may (or may not) be related to this is :
t_dynamical ≈ √R³/GM

The Attempt at a Solution

I'm not sure how to begin, I thought perhaps I could make an equation of motion for an outer shell and equate this to some kind of pressure but I don't know how/ am quite lost.

Any help would be much appreciated thanks.

 

[mfb]

Did you try dimensional analysis?

You cannot use G if you should ignore gravity.