Rotating disks

Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed \(\omega\) . The discs are in the same horizontal plane. At time \(t = 0\), the points \(P\) and \(Q\) are facing each other as shown in the figure. The relative speed between the two points \(P\) and \(Q\) is \(v_r\). In one time period \((T)\) of rotation of the discs, \(v_r\) as a function of time is best represented by

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