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 =A cos (omega t).` There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is ..................

Answer

A, B

Explanation

`x= A cos omega t rArr (dx)/(dt) =-A omega sin omega t rArr (d^(2)x)/(dt^(2)) =-Aomega^(2) cos omega t`
|Max acceleration| `=A omega^(2) therefore alpha_("max") =(Aomega^(2))/R`
Max torque = `Ialpha_("max")=1/2MR^(2)`