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A particle is released on a vertical smooth semicircular track from point X so that OX make angle θ from the vertical (see figure) .The normal reaction of the track on the particle vanishes at point Y where OY makes angle ϕ with the horizontal .Then :

(a)sinϕ=cosθ(b)sinϕ=12cosθ(c)sinϕ=23cosθ(d)sinϕ=34cosθ

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