Rotation 3 Question 19

24. A cylinder of mass M and radius R is resting on a horizontal platform (which is parallel to the xy 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(ωt). There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is

(1988,2M)

True / False

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Answer:

Correct Answer: 24. 13MRAω2 25. F

Solution:

  1. Considering the motion of cylinder.

a=fMα=fRMR22=2fMRRα=2fM or  Now, a+Rα=amax=ω2A

From Eqs. (i) and (ii), v1v2=1 i.e. v1=v2

or both will reach simultaneously.

NOTE In the question,

K= kinetic energy given to ring and cylinder,

KR= rotational kinetic energy and

KT= translational kinetic energy.



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