1. He puts a collar around his dog before walking it.

2. He puts a collar on his dog before walking it.
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Are both OK? Do we have to use 'around' or 'on'? Can we use other verbs instead of 'puts'?

"around" is rather vague. Does he put it around the dog's neck, it's abdomen, it's tail? Usually a collar does go on the neck, so I prefer #2.