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A cylinder of mass M and radius R is res...

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 ___.

Text Solution

Verified by Experts

The correct Answer is:
A, B
`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)`
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