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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
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 $\left.0.4\right]$

  • A
    $\frac{7}{2}\, mg$
  • B
    $5\, mg$
  • ✓
    $\frac{ mg }{5}$
  • D
    $0$
✓

Answer

Correct option: C.
$\frac{ mg }{5}$
c
Let's take solid cylinder is in equilibrium

$T + f = mg \sin 60......(i)$

$TR - fR =0......(ii)$

Solving we get

$T = f _{ seq }=\frac{ mg \sin \theta}{2}$

But limiting friction $ < $ required friction

$\mu mg \cos 60^{\circ} < \frac{ mg \sin 60^{\circ}}{2}$

$\therefore$ Hence cylinder will not remain in equilibrium

Hence $f =$ kinetic

$=\mu_{ k } N$

$=\mu_{ k } mg \cos 60^{\circ}$

$=\frac{ mg }{5}$

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