KVPY SX SB Exam 19-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 the fixed axis AB. A bullet of mass m ( < < M) and speed v is shot horizontally at the face opposite to ABCD at a height 'h' above the surface to impart the cube an angular speed ${\mathit{\omega }}_{\mathit{c}}$ so that the cube just topples over. Then ${\mathit{\omega }}_{\mathit{c}}$ is (note : the moment of inertia of the cube about an axis perpendicular to the face and passing through the center of mass is 2Ma${}^3$ /3)