Small cut in the tyre right beside rim. Should I be worried?

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That doesn't look good to me!

I would be; note that the damage has chipped the alloy as well as cutting the tyre wall.

That's not good surely, will be a weak point as tyres get hotter and expand, would fail an mot I'm pretty sure about that.

Won't fail MOT unless you can see the threads inside the cut.

This is a cut in the thicker rimprotector and unless very deep is no structural problem. I had this after a slow speed contact with a curb at a petrol station. Very annoying and unaesthetic.

Look for any sign of cords or metal in there. If there is, tyre goes in the bin.

Exactly the same as mine. Got home tonight and exactly the same thing. No alloy damage though!

My old Mot testing station would probably try to fail that.

Judging just by the photo, it looks quite deep and would be getting a ticket I think if stopped by the plod.

Peel it back.  If it has cut through cords (string-like stuff) then it's a throw-away.

 

I have something very similar on my tyre (previous owner did it) without cord damage - I've done 30,000km with it like that.

If nothing else keep an eye on it as it could turn into an egg if the side wall is compromised.

Don't worry about, a small nick won't do any harm.

Risk of it going - some on this thread say don't worry about it.

 

Impact of it letting go - personally I would replace it. Or at best keep it in the boot as a spare.

 

My reaction if you keep it on the car and it lets go, and you hit me? - unprintable!

I did 18K miles on a tyre with damage like that. I had it inspected by a local tyre place and they said its fine. The rim protection built into the tyre is designed to do exactly what has happened, the tyre is much thicker at that point. As long as you cannot see any cords it will be perfectly fine, and I guess could have been there for a long time already. 

 As long as you cannot see any cords it will be perfectly fine,

^^^^^ This ^^^^^^