A cylinder of radius R is spinned and then placed on an incline having coefficient of friction $\mathrm{\mu } = \mathrm{tan\theta }$ ($\mathrm{\theta }$ is the angle of incline). The cylinder continues to spin without falling for time :

• A

  $\frac{{\mathrm{R\omega }}_0}{3\mathrm{gsin}\mathrm{\theta }}$

• B

  $\frac{{\mathrm{R\omega }}_0}{2\mathrm{gsin}\mathrm{\theta }}$

• C

  $\frac{{\mathrm{R\omega }}_0}{\mathrm{gsin}\mathrm{\theta }}$

• D

  $\frac{2{\mathrm{R\omega }}_0}{\mathrm{gsin}\mathrm{\theta }}$