Two identical discs, each of negligible mass and radius $r (< < < l)$ are connected by a uniform rod of mass m and length $l$ as shown in the figure. The discs A is connected with an ideal spring of spring constant k at its centre. The spring is un–stretched when $θ = 0^{0} .$ There is no slipping at any contact at any point of time during the motion. Choose the correct statement. [Spring always obeys Hook’s law and mg = $k l$ ]. During the motion, each disc remains in contact with the contact surface.

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The value of $θ,$ when the system is in stable equilibrium is $30^{0}$

The angular speed of the rod when it passes through the position of the stable equilibrium is $\sqrt{\frac{3 g}{4 l}}$

The value of $θ,$ when the system is in stable equilibrium is $60^{0}$

Spring potential energy of the system in the state of stable equilibrium is $\frac{k l^{2}}{8}$

answer is A, C, D.

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Detailed Solution

No friction acts on discs.

$m g = N_{2} + K l (1 - \cos θ)$

For torque $m g \frac{l}{2} \sin θ = K l (1 - \cos θ) \sin θ$

$∴ θ = 60^{0}$

$P . E = \frac{K l^{2}}{8}, W = \sqrt{\frac{3 g}{4 l}}$

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