Can bramin's only belongs to baradwaja gotra?

No, Brahmins can belong to various gotras, not just Baradwaja. Gotra refers to a lineage or clan system in Hindu society, and there are numerous gotras among Brahmins, each representing different ancient sages or rishis. Baradwaja is one of many gotras within the Brahmin community, indicating a specific ancestral lineage.