A circular wooden loop of mass m and radius R rest on a flat horizontal friction less surface. A bullet, also of mass m, and moving with a velocity V, strikes the loop and gets embedded in it. The thickness of the loop is much smaller than R. The angular velocity with which the system angular velocity with which the system rotates just after the bullet strikes the loop is

Question

 

\[\begin {array} {1 1} (a)\;\frac{v}{4}R & \quad (b)\;\frac{v}{3}R \\ (c)\;\frac{2v}{3}R & \quad  (d)\;\frac{3v}{4R} \end {array}\]