Toppling

A football of radius $R$ is kept on a hole of radius $r\ (r < R)$ made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $\theta$ from the horizontal as shown in the figure below. The maximum value of $\theta$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $\sqrt3$. The inclination $\theta$ of this inclined plane from the horizontal plane is gradually increased from 0°. Then