The radii of young ( \lesssim 100 { Myr } ) star clusters correlate only weakly with their masses .
This shallow relation has been used to argue that impulsive tidal perturbations , or ‘ shocks ’ , by passing giant molecular clouds ( GMCs ) preferentially disrupt low-mass clusters .
We show that this mass-radius relation is in fact the result of the combined effect of two-body relaxation and repeated tidal shocks .
Clusters in a broad range of environments including those like the solar neighbourhood evolve towards a typical radius of a few parsecs , as observed , independent of the initial radius .
This equilibrium mass-radius relation is the result of a competition between expansion by relaxation and shrinking due to shocks .
Interactions with GMCs are more disruptive for low-mass clusters , which helps to evolve the globular cluster mass function ( GCMF ) .
However , the properties of the interstellar medium in high-redshift galaxies required to establish a universal GCMF shape are more extreme than previously derived , challenging the idea that all GCs formed with the same power-law mass function .