A uniform rope of mass per unit length $\lambda$, length $\ell$ is attached to shaft that is rotating at constant angular velocity $\omega$. Find the tension in the rope as a function of distance from the shaft. You may ignore the effect of gravitation.
In its solution, we can consider any general differential element $dx$ at a distance $x$ from the axis of rotation, and obtain the equation
$$ -dT=\lambda \omega^2 x dx $$
Once, we integrate it, we does it from $x$ to $\ell$ and take the corresponding tension from $T(x)$ to $0$.
But can anyone tell why $T(\ell) = 0$, cause without tension at the extreme end what can provide the the mass $dm$(at the extreme) the required centripetal force?
By the way , final answer is