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.

Question

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. <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-bpbsok1sshqd.png" /> (A)  textMa (B) ( textMa/2) (C) ( textMa/3) (D)  textMg

Tardigrade Admin · Accepted Answer

For no slipping at P texta1 + textÎ± R = texta arrow (1) Solution

textf = ( textMa)1 = textM ( texta - textÎ± R) arrow (2) textf. R = textI ⋅ textÎ± = ( textMR2/2) ⋅ textÎ± arrow (3) Solve the equations (2) and (3) textf = ( textMa/3) â

Q. 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.

$Ma$

$\frac{Ma}{2}$

$\frac{Ma}{3}$

$Mg$

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

$f = (Ma)_{1} = M (a - α R) \to$ (2)
$f. R = I \cdot α = \frac{MR ^{2}}{2} \cdot α \to$ (3)
Solve the equations (2) and (3)
$f = \frac{Ma}{3}$

Q. 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.

Ma

2Ma​

3Ma​

Mg