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A uniform rod of length $' l'$ and a solid cylinder of radius $' r'$ is kept on a rough inclined plane as shown in the figure. The rod is pivoted, while the cylinder can roll without slipping. A light string PQ attaches top of cylinder to some point on the rod such that string is parallel to the incline. The minimum value of radius of cylinder to ensure that the string is taut when the system is released from rest is

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$\frac{2}{5} l$

$\frac{21}{50} l$

$\frac{4}{9} l$

$\frac{8}{9} l$

answer is C.

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Detailed Solution

$a_{Q} > a_{P} \frac{3 g r \sin θ}{l} > \frac{4}{3} g \sin θ \Rightarrow r > \frac{4 l}{9}$

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