Grófi úrgangurinn er þungur.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.

• úrgangur = waste
• úrgangurinn = the waste

Here, -inn is the definite ending for a masculine singular noun in the nominative.

Because the adjective is placed before a definite noun. In that position, Icelandic adjectives normally take the weak form.

The dictionary form is grófur, but before a masculine singular definite noun it becomes grófi:

• grófur úrgangur = coarse/bulky waste
• grófi úrgangurinn = the coarse/bulky waste

This is a very common pattern in Icelandic:

• góður bíll = a good car
• góði bíllinn = the good car

Because þungur is a predicate adjective, not an adjective directly in front of the noun.

In Grófi úrgangurinn er þungur, the word þungur comes after er and describes the subject. Predicate adjectives usually appear in the strong form, even when the subject is definite.

So:

• grófi úrgangurinn = the coarse/bulky waste
• er þungur = is heavy

A useful comparison:

• góði bíllinn = the good car
• bíllinn er góður = the car is good

Úrgangurinn is:

• masculine
• singular
• nominative

It is nominative because it is the subject of the sentence.

Both adjectives agree with it in gender, number, and case:

• grófi = masculine singular nominative, weak
• þungur = masculine singular nominative, strong

So the two adjectives match the same noun, but they use different declension types because they are in different grammatical positions.

In general, grófur can mean coarse, rough, or not fine. With úrgangur, it often means something like coarse waste or bulky waste, depending on context.

So the exact English wording can vary a bit by situation. In waste-management contexts, it often refers to larger or rougher material, not fine or small waste.

The difference is mainly definiteness:

• grófur úrgangur = coarse/bulky waste, in a general or indefinite sense
• grófi úrgangurinn = the coarse/bulky waste, a specific one already known from context

So the sentence is not talking about waste in general. It is talking about a particular, definite waste item or category.

Yes. That would be a natural sentence too.

The difference is structural:

• Grófi úrgangurinn er þungur
  = the coarse/bulky waste is heavy

• Úrgangurinn er grófur og þungur
  = the waste is coarse/bulky and heavy

In the first sentence, grófi is part of the noun phrase. In the second, grófur is part of the predicate, just like þungur.

The letter þ is pronounced like the th in thing, not like the th in this.

So þungur starts with that unvoiced th sound.

A very rough guide:

• þ = th in thin

This letter is called thorn and is very common in Icelandic.