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A cylinder of mass M rests on a rough horizontal rug that is pulled out from under it with acceleration a perpendicular to the axis of the cylinder. If the cylinder does not slip, the friction force at the contact point P is

Asked in JEE Main Online 2014 · Rolling dynamics and slipping

Answer: (4) (Ma)/3

Step-by-step solution

Let the cylinder's centre acceleration be a_c and angular acceleration α. Friction f is the only horizontal force: f=Ma_c, and fR=1/2 MR²α.

The no-slip condition at the accelerating rug gives a_c=a/3, so f=Ma_c=(Ma)/3.

Why the other options are wrong

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