Question
A solid cylinder is placed on a rough surface of inclination $\theta $ , minimum value of coefficient of static friction between the cylinder and the surface so that the cylinder roll's without slipping is
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Answer
$a=\frac{g \sin \theta}{\left(1+\frac{k^{2}}{R^{2}}\right)}$
$\Rightarrow g \sin \theta-\mu g \cos \theta=\frac{g \sin \theta}{\left(1+\frac{1}{2}\right)}$
$\Rightarrow \frac{1}{3} g \sin \theta=\mu g \cos \theta$
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