What is the monetary value of a 1911 mercury dime with a V on the back?

My strong guess is that your "dime" is actually the same size and thickness as a nickel, because .................. it IS a nickel. The "V" is of course the Roman numeral meaning 5.

In addition, it's not made of silver, but an alloy of copper and nickel, AND it could not have the so-called Mercury design because that wasn't introduced until 1916.

What you have is called a Liberty nickel. 1911 is a fairly common year: In worn condition it retails for about $3. With moderate wear, about $10, and with almost no wear, $30.