A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the cylinder has a translational velocity $v_0=49 \mathrm{~m} / \mathrm{s}$, perpendicular to its axis and a rotational velocity $v_0 / 4 R$ about the centre. The time taken by the cylinder to start rolling is $\_\_\_\_$ seconds. (coefficient of kinetic friction $\mu_{\mathrm{K}}=0.25$ and $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$ )
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