Is following grammar LR(0)?
You haven't actually augmented the grammar. The augmented grammar has the production $$start\to SL\;\$$$

With that change, state 1 is not a reduction state and there is no conflict.

If you did not intend to augment the grammar, then it is not $LR(0)$, because the language does not have the prefix property. But that's not very useful, so normally we augment grammars, turning the language $L$ into $L\$$, where $\$$ is a symbol not in the the alphabet for $L$. Clearly the augmented language has the prefix property.

There's a reasonable explanation with references on Wikipedia.