A particle of mass m is resting on the inside of a smooth, circular hoop of radius

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A particle of mass m is resting on the inside of a smooth, circular hoop of radius 3a. The particle is then projected from the lowest point, with horizontal speed u.

a. State the minimum speed required to complete vertical circles.

b. The particle is projected with speed √12ga. Find the speed when the particle has turned through 120°.

c. Find also the reaction force exerted on the particle when the angle is 120°.

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