is there any need to index b again as it is already a under primary Is there any need to index b again as it is already a  under primary-
if primary(a,b)  and in query we have where b=' '; 

Is there any need to index(b) again individually because while indexing it will take left column first then thinks of the next.

Thanks in advance!, and please help me out of this.
If you have index on (a,b) and a query with b = ? then that query can't make efficient use of that index. There are DBMS that can make use of the index in a decent way, but mysql is not one of those.