Roatation

Q. A cylinder of mass $M$, radius $R$ is resting on a horizontal platform (which is parallel to $xy-$plane) with its axis fixed along the $y-$axis and only free to rotate about its axis. The platform is given a motion in $x-$direction given by $x=A\cos \left(\omega t\right)$. There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is

1. $\frac{1}{2}MRA{\omega }^2$
2. $MRA{\omega }^2$
3. $2MRA{\omega }^2$
4. $MRA{\omega }^2\times \cos \omega t$

Q. A cylinder of mass $M$, radius $R$ is resting on a horizontal platform (which is parallel to $xy-$plane) with its axis fixed along the $y-$axis and only free to rotate about its axis. The platform is given a motion in $x-$direction given by $x=A\cos \left(\omega t\right)$. There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is

1. $\frac{1}{2}MRA{\omega }^2$
2. $MRA{\omega }^2$
3. $2MRA{\omega }^2$
4. $MRA{\omega }^2\times \cos \omega t$