What is the exact mm of uv filter lens for my nikon D5100 with 18-105mm lens?

I have nikon d5100 and with AF-S DX ZOOM-NIKKOR 18-105mm f/3.5-5.6 G ED VR lens.
pl tell me the exact size of uv filter.
secondly, is it necessary to fix a filter and why?

67mm diameter filters are required for your lens. It says so right on the lens barrel as well as in the Owner's Manual for the lens.

A good quality UV filter protects the front element of your lens. Choose from B+W, Tiffen or Hoya.

Always remember: "A cheap filter isn't good and a good filter isn't cheap."

"secondly, is it necessary to fix a filter and why?"

No, it's not. In fact, it's better NOT to.
A UV filter will do nothing as a filter for your shots -- modern digital sensors aren't UV sensitive at all, unlike films were. So the "UV" filtering does absolutely nothing.
All you're doing is putting a cheap piece of flat glass in front of an expensive lens, degrading image quality and providing two more glass-air surfaces for reflections to occur on. The "protective" value of such a filter is questionable at best, and it will *always* degrade image quality -- sometimes only a tiny bit, other times significantly. There's no reason to put one on unless you're going to be shooting in blowing sand or dust, or at the ocean in salt-water spray.

Next time you see a bunch of pro photographers at a sporting event, with hundreds of pro-level cameras and lenses, take a good look at them: you won't find *any* of them using a "protective UV filter." There's a good reason for that.