Consider a cylinder of mass M resting on a rough horizontal rug that… | JEE Main 2014 (19 Apr, Shift 1)

Q78JEE Main 2014 · 19 APR · SHIFT 1Difficult

Rolling Motion

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is Ffriction at point P? It is assumed that the cylinder does not slip.

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Answer: (d)

Friction $f$ on the cylinder points along $a$ : centre acceleration $a_c = \dfrac{f}{M}$ .
Torque: $fR = \frac{1}{2}MR^2\alpha \Rightarrow \alpha R = \dfrac{2f}{M}$ .
No slipping: acceleration of P equals the rug's, $a_c + \alpha R = a \Rightarrow \dfrac{3f}{M} = a$ .
$f = \dfrac{Ma}{3}$ , so the answer is (d).

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Rolling Motion question from JEE Main 2014 (19 Apr, Shift 1)

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