Admittedly, I could have clarified a couple more rules to the question and another one more option to the list of possible answers. I.e. The force is both unstoppable and unchanging. The object is both immovable and indestructible. That our current understanding of physics cannot be broken when thinking of the question. And this forth option for the strict realists: "Neither exists and therefore do not want to entertain the question".

Anyway, the video posted by phxbillcee below explains this thought experiment well.

Thanks to everyone who replied.

I don't think either exist. Everything moves and there is no unstoppable force.

I believe in that event both items would convert instantly to energy. I'd advise being a little way off for safe viewing.

In reality, there exist neither unstoppable forces nor immovable objects, so the question is meaningless. Might as well ask if a dragon can gargle unicorn milk.