The ball has mass M and a negligible size. It is originally traveling around the horizontal circular path of radius r₀ such that the angular rate of rotation is θ'₀. If the attached cord ABC is drawn down through the hole at constant speed v, determine the tension the cord exerts on the ball at the instant r = r₁. Also, compute the angular velocity of the ball at this instant. Neglect the effects of friction between the ball and horizontal plane. First show that the equation of motion in the θ direction yields a_θ = rθ'' + 2r' θ' =(1/r)(d(r²θ')/dt) = 0.When integrated, r² θ' = c where the constant c is determined from the problem data.

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Given: M = 2 kg ro = 0.5 m 00 = 1 V = 0.2 rad S m S r1 = 0.25 m