A block of mass m is placed on a rough parabolic surface $y = \frac{x ^{2}}{4}$ , where x and y are in meter. The coefficient of friction between block and surface is 0.5 . If block is released from rest at point P then y-coordinate of the point P if relative slipping between block & surface just takes place is :

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At the point of just slipping, tan θ = μ = 0.5 . For y = 4 x 2 ​ , slope d x d y ​ = 2 x ​ = tan θ = 0.5 , so x = 1 m. Then y = 4 x 2 ​ = 0.25 m . Hence option (A).

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