Rotating Gears

Two gears \(A\) and \(B\) are meshing together as shown above. The numbers of cogs on each gear are \(12\) and \(24\), respectively, and \(3\) red dots \(x,\) \(y\) and \(z\) are marked on the two gears. Both gears are in uniform circular motion, and the radii of the rotating circles \(x\), \(y\) and \(z\) are \(r\), \(2r\) and \(r\), respectively. Which of the following statements is correct?

a) The period of point \(x\) is the same as that of point \(z\).
b) The angular speed of point \(x\) is greater than that of point \(y\).
c) The magnitude of acceleration of point \(y\) is greater than that of point \(z\).

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