InterviewSolution
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InterviewSolution
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A cylinder of mass M and radius R is resting on a horizontal paltform (which is parallel to the x-y plane) with its exis 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 acitng on the cylinder during its motion is .................. |
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Answer» Correct Answer - A::B::C Considering the motion of the platform `x=A cos omegat` `rArr (dx)/(dt) =- A omega sin omegat rArr(d^2x)/(dt^2) =- A omega^2 con omegat` The magnitude of the maximum acceleration of the platform is `:. |Max acceleration| = A omega^2` When platform moves a torque acts on the cylinder and the cylinder rotates about its exis. Acceleration of cylinder, `a_1 = (f)/(m)` Torque `pi = fR :. l alpha = fR` `alpha = (fR)/(I) = (fr)/(MR^2 /2)` or, `alpha = (2f)/(MR) or Ralpha = (2f)/(M)` `:. Equivalent linear acceleration (Ralpha = a_2)` `a_2 = (2f)/(M)` :. Total linear acceleration, `a_(max) = a_1 +a_2 = (f)/(M)+(2f)/(M) = (3f)/(M)` or,`Aomega^2 = (3f)/(M) or , f = (MAomega^2)/(3)` Thus, maximum torque, `tau_(max) = fxxR = (MAomega^2R)/(3) = (1)/(3) MARomega^2` |
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