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 disc A is connected with an ideal spring of spring c

Question

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 disc A is connected with an ideal spring of spring constant k at its centre. The spring is unstretched when θ = 0 ∘ . There is no slipping at any contact at any point of time during the motion. Choose the correct statement(s) [Spring always obeys Hook's Law and mg = k ℓ ]. During the motion, each disc remains in contact with the contact surface :-

TestHub · Accepted Answer

Spring stretch: y = ℓ ( 1 − cos θ ) . U = 2 1 ​ k y 2 + m g [ 2 ℓ c o s θ ​ + y − 2 ℓ ​ ] ; d θ d U ​ = 0 ⇒ θ = 6 0 ∘ with d θ 2 d 2 U ​ > 0 - stable equilibrium at 6 0 ∘ - (A) Spring PE at θ = 6 0 ∘ : 2 1 ​ k [ ℓ ( 1 − cos 6 0 ∘ ) ] 2 = 8 k ℓ 2 ​ = 8 m g ℓ ​ (using m g = k ℓ ) - (C) The angular speed at the equilibrium position follows from energy conservation between θ = 0 ∘ and 6 0 ∘ - (D)

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