A cylinder of mass `M` and radius `R` is resting on a horizontal platform (which is parallel to the `x-y` plane) with its axis fixed along the `y`-axis and free to rotate about its axis. The platform is given a motion in the `x`-direction given by `x=Acos(omegat)` There is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder during its motion is ___.

Explanation

`x = A cos omaga t`
`nu = (dx)/(dt) = - A omega sin omega t`
`a = (d^(2)x)/(dt^(2)) = - A omega^(2) cos omega t`
`a_(max) = A omega^(2)`
`tau_(max) = 1 alpha_(max)`
`= l (a_(max))/( R)`
`= (m R^(2))/(2) A omega^(2)/( R) = (MRA omega^(2))/(2) = 6 N-m`