Question 267 of 280

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.

A$\text{Ma}$B$\dfrac{\text{Ma}}{2}$C$\dfrac{\text{Ma}}{3}$D$\text{Mg}$

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Answer: (C) $\dfrac{\text{Ma}}{3}$

For no slipping at P
${\text{a}}_{1}+\text{α}R=\text{a}\rightarrow$ (1)



$\text{f}={\text{Ma}}_{1}=\text{M}\left(\text{a}-\text{α}R\right)\rightarrow$ (2)

$\text{f. R}=\text{I}\cdot \text{α}=\dfrac{{\text{MR}}^{2}}{2}\cdot \text{α}\rightarrow$ (3)

Solve the equations (2) and (3)

$\text{f}=\dfrac{\text{Ma}}{3}$ ​