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, $\mu_{\mathrm{s}}$, is $\left.0.4\right]$
Correct Option: , 3
Let's take solid cylinder is in equilibrium
$T+f=m g \sin 60$ ...................(1)
$\mathrm{TR}-\mathrm{fR}=0$ ................(2)
Solving we get
$\mathrm{T}=\mathrm{f}_{\mathrm{req}}=\frac{\mathrm{mg} \sin \theta}{2}$
But limiting friction $<$ required friction
$\mu \mathrm{mg} \cos 60^{\circ}<\frac{\mathrm{mg} \sin 60^{\circ}}{2}$
$\therefore$ Hence cylinder will not remain in equilibrium
Hence $f=$ kinetic
$=\mu_{\mathrm{k}} \mathrm{N}$
$=\mu_{\mathrm{k}} m g \cos 60^{\circ}$
$=\frac{m g}{5}$
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