question_answer

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:                                                                                                                [JEE Main 09-Jan-2019 Morning]

A)         \[\frac{2\,k\,{{\theta }_{0}}^{2}}{l}\]

B)        \[\frac{k\,{{\theta }_{0}}^{2}}{l}\]

C)   \[\frac{3k\,{{\theta }_{0}}^{2}}{l}\]  

D)        \[\frac{k\,{{\theta }_{0}}^{2}}{2\,l}\]

Correct Answer: B

Solution :

Option   is correct.