JEE Main 2019 — Rotational Motion Question with Solution

Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l.$ The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system (see figure). Because of torsional constant $k,$ the restoring torque is $\tau =k\theta$ for angular displacement $\theta .$ If the rod is rotated by ${\theta }_0$ and released, the tension in it when it passes through its mean position will be: