FX lens on nikon d5100?

I plan on getting the nikon d5100 with the nikon 50mm 1.8g lens which is a FX lens. Will this be a problem? If I'm correct, the d5100 is a dx body.

Yes, and your problem is?

Nikon don't specifically make a DX 50mm lens, because they don't need to - both types fit the D5100 - as your manual will tell you.

The problem comes if the lens isn't motorised, which this one is - AF lenses don't autofocus on the D3000/D5000 series because they lack body motors.AF-S lenses (like this one) do.

I have a 50mm f1.8 AF-D lens. It works with my Nikon D90. At least it did the last time I used it, which I think is about three years ago. While the FX 50mm prime lens is compatible with DX cameras, I have found the actual situational usefulness to be infrequent. It is much more likely to be a good choice with a FX cameras.

FX lenses generally work perfectly on DX bodies. It's just the opposite that does not apply, DX lenses have operational disadvantages on FX bodies (not using the full sensor size).

What needs to be considered is that your camera doesn't have an autofocus motor, it depends on the lens to bring it. The 50mm/1.8G lens happens to be an AF-S lens, so it has its own autofocus motor and thus will work perfectly on your camera. Some older lenses, e.g. The 50mm/1.8D, are just AF and not AF-S. These depend on an autofocus motor in the camera (present in e.g. D90, D7000 and so on, but not D5100)

Since the 50mm lens in question is an AF-S lens it will auto focus and function just fine on your D5100. However, due to the 1.5x "crop factor" of the DX body, the 50mm lens on your D5100 will have the equivalent angle of view of a 75mm lens on a full-frame (D600, D800, D4) DSLR. This makes the 50mm lens on your D5100 a good choice for portraits but may prove problematic when used indoors in small spaces. It is, however, a good choice for available light photography indoors.

However, I suggest buying the D5100 with the usual 18-55mm f3.5-5.6G zoom and buying the 50mm f1.8G separately. I believe you'll find the 50mm lens isn't versatile enough for your needs. The 18-55mm zoom will give you more options in your day to day photography and then you can switch to the 50mm f1.8 in low-light situations or when you want to try taking portraits.

Yes, it will work fine.