Why is that this way

The first sentence,

Your rope is going to tear.

is correct.

The second sentence,

Your rope is going to be torn.

is incorrect because to be comes before torn - the past tense of the word tear, when to be should be used to describe something in the future. To be should not come before torn - the past form of what is going to happen to the rope.

1) Your rope is going to tear!

And

2) Your rope is going to be torn!

In the first case to me it seems like the rope is going to tear something or somebody. In the second one I just feel doesn't sound natural.

Which one is right and why?

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The first one as it stands is correct, although I would say that to my ear (note I am British) the use of tear connected with rope sounds strange. Normally we would use Break.

Your rope is going to tear!

meaning

Your rope [noun], is, go-ing [verb] (HAPPEN-ing), to, be pulled apart

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The second one I agree doesn't sound natural, it has something missing.

Your rope is going to be torn.

However I think this works much better.

Your rope is going to be torn apart

Example Cambridge English Dictionary

Concerns that moral fabric and cohesiveness of society will be torn apart provide reasons for care and reflection.

However why tear/torn should sound strange is a little bit of a mystery. I would suggest that there is a reason albeit a subtle connection. Which is made clear when you substitute the noun.

Your jacket is going to be torn

Your hand is going to be torn (to bits).

Your family is going to be torn (apart)

Your newspaper is going to be torn

Your photo is going to be torn (out)

Tear/Torn is often used alongside another verb, torn apart. torn to pieces, torn to bits, torn to ribbons, to shreds etc the Cambridge Thesaurus lists many relate words.

I think both could be correct:

"Your rope is going to break!"

(I agree I would not use 'tear' with a rope - tear is more applicable to a sheet, of fabric or paper...)

This phrase could be said as a warning if one rock climber had seen his friend's rope starting to fray (fibres begin to break) after rubbing on a sharp rock.

"Your rope is going to be broken!" is an unusual use of English, in that it is not complete...

This phrase is less urgent than the first and could be used to express a predicted future event, for example: "Your rope is going to be broken [torn] by the sharp rocks!"

However, it would probably not be used in this form as, on its own, it does not give enough information. It would probably be used with an 'IF' statement, something like:

"If you hang your rope over that edge, it will break [because the sharp rock edge will cut through it...]"