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 inclin

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, μ s , is 0 . 4 ]

TestHub · Accepted Answer

Let's take solid cylinder is in equilibrium

$T + f = m g \sin 60$

$T R - f R = 0$

Solving we get

$T = f_{r e q} = \frac{m g \sin θ}{2}$

But limiting friction $<$ required friction

$μ m g \cos 60 ° < \frac{mg \sin 60 °}{2}$

$∴$ Hence cylinder will not remain in equilibrium

Hence $f =$ kinetic

$= μ_{k} N$

$= μ_{k} m g \cos 60 °$

$= \frac{m g}{5}$

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