$A$ cylinder of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. $A$ particle of mass $m$ moving with velocity $v$ hits the cylinder and sticks to its rim. Calculate the angular velocity of the cylinder after the impact.

• A
  $\frac{I\omega + mvR}{I + mR^2}$
• B
  $\frac{I\omega - mvR}{I + mR^2}$
• C
  $\frac{I\omega + mvR}{I - mR^2}$
• D
  $\frac{I\omega + mv}{I + mR}$