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A solid cylinder of mass \( M \) and radius \( R \) is resting on a horizontal platform (which is parallel to the \( x-y \) plane) with
\( \mathrm{P} \) its axis fixed along \( Y \)-axis and free to rotate about its axis.

W. The platform is given a motion in the \( X \)-direction given by \( x=A \cos (\omega t) \). There is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder during its motion is
(1) \( \frac{M \omega^{2} A R}{3} \)
(2) \( \frac{M \omega^{2} A R}{2} \)
(3) \( \frac{2}{3} \times M \omega^{2} A R \)
(4) the situation is not possible
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