A rod is fixed between a vertical wall and a horizontal surface. A smooth ring of mass 1 kg is released from rest which can move along the rod as shown. At the release point spring is vertical and rel

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A rod is fixed between a vertical wall and a horizontal surface. A smooth ring of mass 1 kg is released from rest which can move along the rod as shown. At the release point spring is vertical and relaxed. The natural length of the spring is ( 3 ​ + 1 ) m ( g = 10 m / s 2 ) Rod makes an angle of 30° with the horizontal. Ring again comes to rest when spring makes an angle of 30° with the vertical.

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Geometry: spring extension x = 2 m, ring displacement d = 3 ​ − 1 2 ​ m. Energy: m g d sin 3 0 ∘ = 2 1 ​ k x 2 k = 2 5 ​ ( 3 ​ + 1 ) N/m. Normal: N = m g cos 3 0 ∘ − k x sin 3 0 ∘ = 2 5 ​ ( 3 ​ − 1 ) N. Extension is 2 m, not 3 ​ − 1 . Answers: (A), (B), (D).

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