Expression for Torsional Pendulum

Q. Torsional stiffness is defined as the torque required to produce a unit angle of twist.

1. False
2. True

Q. A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant α is defined by the relation J = –αθ , where J is the restoring couple and q the angle of twist).

Q. Two masses $m$ and $m/2$ 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 as shown in the figure.
Because of torsional constant $K$, the restoring torque is $\tau =K\theta$ for angular displacement $\theta .$
If the rod is rotated by ${\theta }_{\circ }$ and released so that rod oscillates. The tension in the rod, when it passes through its mean position will be

1. $\frac{3K{\theta }_{\circ }^2}{l}$
2. $\frac{2K{\theta }_{\circ }^2}{l}$
3. $\frac{K{\theta }_{\circ }^2}{l}$
4. $\frac{K{\theta }_{\circ }^2}{2l}$