What is the difference between, "The book was very boring and it belonged in a dustbin" and "The uniform looks like it belonged to a museum collection".
Belong to is generally possessive:
This book belongs to me = This is my book.
Belong in (or on or_under_, etc) indicates that something should be in (or on, or under) a certain position:
This book belongs in a dustbin = This book should be in a dustbin.
In case of the museum collection, actually both are possible, but they have a different meaning:
The uniform looks like it belonged to a museum collection.
It looks like there is a museum that has this uniform in its collection. The uniform looks like it was removed from that collection.
The uniform looks like it belonged in a museum collection.
This uniform may not literally be taken from a museum, but it should be in a museum.
Another example to show the difference:
That car looks like it belongs to John's collection.
The car may have been stolen from John.
That car looks like it belongs in John's collection.
I think John should buy that car. It fits with the rest of his collection.