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: (1) $k \theta _ { 0 } ^ { 2 }$ (2) $\frac { 3 k \theta _ { 0 } { } ^ { 2 } } { l _ { 0 } }$ (3) $\frac { 2 k \theta _ { 0 } { } ^ { 2 } } { l }$ (4) $\frac { k \theta _ { 0 } { } ^ { 2 } } { l }$
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:\\
(1) $k \theta _ { 0 } ^ { 2 }$\\
(2) $\frac { 3 k \theta _ { 0 } { } ^ { 2 } } { l _ { 0 } }$\\
(3) $\frac { 2 k \theta _ { 0 } { } ^ { 2 } } { l }$\\
(4) $\frac { k \theta _ { 0 } { } ^ { 2 } } { l }$