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

Question

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,
$T = m{omega}^{2} x$
I am in confusion....

fibonatic · Accepted 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 $x$.

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

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