# A particle is made to move along a vertical circular path with radius r find the height reached by the bloock over the wedge if there is no friction

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2015-09-11T02:45:48+05:30

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The particle has a velocity v before moving along a vertical circular path of radius r.

Let the center of the circular path be C.  Let the vertical radius through C be CB.  Let A be the point on the circle at which the particle stops finally.  The particle loses speed when it moves up, as gravity decelerates it.

Initial total energy of the particle = K E = 1/2 * m * v²
final total energy of the particle = P E = m g h,  where h = r (1 - Cos θ)
θ is the angle between CB and CA.

we apply the conservation of energy principle.

m g h = 1/2 * m * v²
=> h = r (1 - cos θ) = v² /(2 g)