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@@PaPhysics_Manish sir instead of doing like this please start teaching topics not like questions but only advanced oriented

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From the question particle is moving in the plane having accelerations in the tangential and normal to the tangential acceleration. This implies that the particles moving trajectory is curved path. At any instant of time 't' the curve at which the point lies will have a radius of curvature and that is 'R'. It means at that instant of time the particle will be moving in a circular path having radius 'R'. Now we know that when a particle moves in a circle it's having an acceleration in the radial direction towards its center. This is what is w_n which is equal to v^2/R.

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