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 `(ltltM)` 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 `omega_(c)` so that the cube just topples over. Then `omega_(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`)

Options

A. `sqrt(3gM//2ma)`
B. `sqrt(3g//4h)`
C. `sqrt(3g(sqrt2-1)//2a)`
D. `sqrt(3g(sqrt2-1)//4a)`

Answer

D