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QuestionPhysicsClass 11

A cylinder of radius $${R}$$ and mass $${M}$$ rolls without slipping down a plane inclined at an angle $$\theta$$. Coeff. of friction between the cylinder and the plane is $$\mu$$. For what maximum inclination $$\theta$$, the cylinder rolls without slipping ?
(A) $${{\tan}^{{-{1}}}\mu}$$
(B) $${{\tan}^{{-{1}}}{\left({3}\mu\right)}}$$
(C) $${{\tan}^{{-{1}}}{2}}\mu$$
(D) $${{\tan}^{{-{1}}}.}\frac{{{3}}}{{{2}}}\mu$$

As is know from theory,
$$\mu=\frac{{{\tan{\theta}}}}{{{1}+{m}{R}^{{{2}}}/{I}}}=\frac{{{\tan{\theta}}}}{{{1}+{2}}}=\frac{{{\tan{\theta}}}}{{{3}}}$$
$${{\tan{\theta}}_{{\max}}=}{3}\mu$$
$$\theta_{{\max}}={{\tan}^{{-{1}}}{\left({3}\mu\right)}}$$