A particle is attached to one end of a string, the other end of which is fixed. The particle moves in a vertical plane. The velocity at the lowest point is such that the particle can just complete the circle. The ratio of tension in the string at A and B is :-

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Just completing the circle: v b o tt o m 2 ​ = 5 g ℓ . At A (60° from the downward vertical): v A 2 ​ = 4 g ℓ , T A ​ = ℓ m v A 2 ​ ​ + m g cos 6 0 ∘ = 2 9 m g ​ . At B (60° from the upward vertical): v B 2 ​ = 2 g ℓ , T B ​ = ℓ m v B 2 ​ ​ − m g cos 6 0 ∘ = 2 3 m g ​ . Ratio = 3. Hence (B).

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