KVPY SX SB Exam 05-Nov-2017 Question Paper

A solid cube of wood of side 2a and mass M is resting on a horizontal surface as shown in the figure. The cube is free to rotate about a fixed axis AB. A bullet of mass and speed v is shot horizontally at the face opposite to ABCD at a height $\frac{4\mathit{a}}{3}$ from the surface to impart the cube an angular speed ω. It strike the face and embeds in the cube. Then ${\mathit{\omega }}_{\mathit{c}}$ is close to (note : the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is $2\mathit{M}\frac{{\mathit{a}}^2}{3})$