If there is physical violence among members of society a government is failing at which of its purpose

The purpose of the government is to "establish Justice, insure domestic Tranquility, provide for the common defence, and promote the general welfare."

So, mostly everything to do with society's welfare.

The Government is the social organization created to basically set up and enforce public policies such as maintaining the order by establishing justice promoting the rule of law, protecting the nation by common defense, promoting general welfare supporting the economic system and protecting people's rights. If physical violence rises, the government is failing at maintaining the order and promoting the rule of law.