Question

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is :

[The coefficient of static friction, ${\mu }_s$, is $0.4]$

• A. $\frac{7}{2}mg$
• B. $5mg$
• C. $\frac{mg}{5}$
• D. 0

Answer 1

Answer: (C)

Let's take solid cylinder is in equilibrium
$T+f=mg\sin 60\dots (i)$
$TR-fR=0\dots (ii)$
Solving we get
$T=f_{\text{seq }}=\frac{mg\sin \theta }{2}$
But limiting friction $<$ required friction
$\mu mgcos60^{\circ }<\frac{mg\sin 60^{\circ }}{2}$
$\therefore$ Hence cylinder will not remain in equilibrium
Hence $f=$ kinetic
$={\mu }_{k}N$
$={\mu }_{k}mgcos60^{\circ }$
$=\frac{mg}{5}$