Tilting a table Let us say we have a perfectly horizontal table which has a cube placed on top of it. Furthermore, the cube is hollow and the sides weight is negligible. Now, what is the maximum angle that I can tilt the table such that the cube won't tumble on another side. 
My intuition tells me that angle should be less than 45 degrees. Because a cube is a symmetrical shape and 45 degrees would "perfectly" balance the cube on a edge/side (not a face).
Finally, would friction or the side length of the cube matter?
Is my intuition correct?
 A: The forces acting on the box will be those by 'gravity', the normal reaction force by the table and the friction force by the table. The force of gravity has two components (passing through the center of inertial mass owing to the equivalence principle) along the surface of the table and normal to it. The friction acts along the surface and the normal reaction force is, of course, normal to the surface. 
Now the component of gravitational force along the surface produces a torque about a horizontal axis that lies on the surface of the table and intersects the line of action of the normal component of the gravitational force. To balance this torque, the line of action of the normal reaction gets a bit shifted from that of the normal component of gravitational force. But there is a limitation to how much the line of action of the normal reaction force can shift. Namely, it must remain within the dimensions of the cube. Considering this limit, one can arrive at the conclusion that beyond a certain angle of tilt that depends on the dimensions of the cube, the cube must topple. 
Hint The mass doesn't remain in the final expression because the torque by the component of gravity along the surface and the torque due to the normal reaction force are both directly proportional to the mass and thus equating them cancels out the term of mass. 
