Question

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 ..................
A. `(Momega^(2)AR)/3`
B. `(Momega^(2)AR)/2`
C. `2/3xxMomega^(2)AR`
D. The situation is not possible

Answer 1

Correct Answer - B
The cylinder is having a fixed axis, so it can perform rotational motion only.

`fR=(MR^(2))/2alphaimpliesf=(MR)/2alpha`
For no slipping,
`Ralpha=` acceleration of the platform
`(2f)/M=omega^(2)Acosomegat`
For the maximum torque `f` would maximum and `f_(max)=Momega^(2)A/2`
So the maximum torque,
`tau_(max)=f_(max)xxR-=(M^(2)omega^(2)AR)/2`