The 3-kg collar B slides on the frictionless arm AA’. The arm is attached to drum D and rotates about O in a horizontal plane at the rate = 0.75t, where  and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within the drum releases cord so that the collar moves outward from O with a constant speed of 0.5 m/s. Knowing that at t = 0, r = 0, determine the time at which the tension in the cord is equal to the magnitude of the horizontal force exerted on B by arm AA’.

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B