homework and exercises - A rod of length $L$ & mass $M$ is rotating in a circle about one end then calculate tension in the rod at a distance $x$ from the support

A rod of length L & mass M is rotating in a circle about one end then calculate tension in the rod at a distance 'x' from the support ?

For its solution why should we take mass of L-x portion of rod instead of taking mass upto x distance from support as we have the formula

T = m w2 x I m in confusion....

Answer

You have to take the mass from $L$ to $x$, since that is the mass which has to be accelerated by the centripetal force due to the tension at position $x$. The remaining mass of the rod (before position $x$) doesn't add anything to the tension in $x$.