A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia Vs I, radius R, and initial angular velocity w as shown in the figure. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular veloity of the merry-go-round 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. \[\frac{I\omega -mvR}{I}\]
• D. \[\frac{(I\omega -m{{R}^{2}})\omega -mvR}{I}\]