The acid in your stomach is ~0.1M. Assuming you're talking about a thumb tack with a metal and plastic part you've got a few issues.
Given long enough (it'll take a while with that weak of an acid) the metal will dissolve...you'll feel the tendancy to burp too, or fart, due to the hydrogen given off by the dissolving metal. The plastic part will not be dissolved in all likely hood....so that will have to come out somewhere.