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_o =49…

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