A block is placed on a rough inclined plane with inclination θ=45∘. The coefficient of static friction between the block and the incline is μ=0.25. Determine the maximum ratio h/b for which the homogenous block will slide without tipping under the action of force F.

Block has to slide without tipping, which implies that block is in translational as well as rotational equilibrium. When the block is on the verge of tipping about edge A, the normal reaction will pass through the edge of the block. From conditions of equilibrium along sloping surface:F+μN=mgsin⁡θ            …(i)Perpendicular to the sloping surface:N=mgcos⁡θ                  …(ii)Balancing torque about point A:F×h=(mgcos⁡θ)b2        …(iii)From Equations, (i), (ii) and (iii), F=mgsin⁡θ−μmgcos⁡θ       …(iv)On substituting F in Eq. (iii), we obtain(mgsin⁡θ−μmgcos⁡θ)h−mgcos⁡θb2=0which on solving for h/b yieldshb=12(tan⁡θ−μ)=12tan⁡45∘−0.75=2.0