Q 11-06-232JEE MainJEE Main 2019 (12 Apr, Shift 1)Medium
A uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis, then which of the following graphs depicts it most closely?
Answer: (C) see figure
The tension at $x$ supplies the centripetal force for the part of the rod beyond $x$ (mass per length $m/l$):
$$T(x) = \int_x^l\frac ml\,\omega^2r\,dr = \frac{m\omega^2}{2l}\left(l^2 - x^2\right)$$
This is maximum at $x = 0$ and falls along a downward parabola to zero at $x = l$: graph (3).
Solution by Sreeraj P, M.Sc Physics