When we have $n$ elements in array, Merge Sort Makes $\Theta (nlogn)$ Comparisons.
When each element is simply Integer, each comparison takes $\Theta(1)$ time, So Merge Sort time complexity becomes $\Theta(n)$ Comparisons $\times \Theta(1)$ time per comparison.
So, $\Theta(nlogn)$ time complexity.
When each element is string of length $P$, each comparison takes $O(P)$ time, So Merge Sort time complexity becomes $ \Theta(nlogn)$ Comparisons $\times O(P)$ time per comparison.
So, $O(P*nlogn)$ time complexity.
For this question $P$ is $n.$
WHY $T(n) = 2T(n/2) + O(n^2)$ is NOT Correct Recurrence Relation for this question??
Answer : Because, in this recurrence relation, one of the $'n'$ in $n^2$ is Not Recurrence variable here.
If you didn't understand this, then assume that each string has length $m.$
Now, Recurrence Relation will be $T(n) = 2T(n/2) + O(mn)$ .. This is correct Recurrence Relation.
NOTE that $m$ is Not Recurrence variable, So, if we put $m=n$ in this equation, we'll make it Recurrence variable which is Wrong.
Basically Open the Recursive equation and at the end of series calculation, put $m =n$.