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

$(a)\;sin \phi=cos \theta\qquad(b)\;sin \phi= \large\frac{1}{2} \normalsize cos \theta\qquad(c)\;sin \phi= \large\frac{2}{3}\normalsize cos \theta\qquad(d)\;sin \phi= \large\frac{3}{4} \normalsize cos \theta$