$A$ child with mass $m$ is standing at the edge of a disc with moment of inertia $I$,radius $R$,and initial angular velocity $\omega$. See the figure given below. The child jumps off the edge of the disc with tangential velocity $v$ with respect to the ground. The new angular velocity of the disc is

• A
  $\sqrt {\frac{{I{\omega ^2} - {m}{v^2}}}{I}} $
• B
  $\sqrt {\frac{{(I + {m}{R^2}){\omega ^2} - {m}{v^2}}}{I}} $
• C
  $\frac{{I\omega - {mv}R}}{I}$
• D
  $\frac{{(I + {m}{R^2})\omega - {mv}R}}{I}$