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 F_friction at point P ? It is assumed that the cylinder does not slip.

• A

  $\text{Ma}$
• B

  $\frac{\text{Ma}}{2}$
• Correct answer
  C

  $\frac{\text{Ma}}{3}$
• D

  $\text{Mg}$

Solution

For no slipping at P
${\text{a}}_1+\text{α}R=\text{a} \to$   (1)



$\text{f}={\text{Ma}}_1=\text{M}\left(\text{a}-\text{α}R\right) \to$   (2)

$\text{f. R}=\text{I}·\text{α}=\frac{{\text{MR}}^2}{2}·\text{α} \to$   (3)

Solve the equations (2) and (3)

$\text{f}=\frac{\text{Ma}}{3}$ ​

Hence, the correct answer is option: 'C'.