Determine the maximum ratio `h//b` for which the homogenous block will side without tipping under the actionof force `P`. The coefficient of static friction between the block and the incline is `mu_(s)`.

Explanation

Block has to slide without tipping, which implies that block is in translational as well as rotational equilibrium.
From conditions of equlibrium,
Along sloping surface.
`F+muN=mgsintheta` ..................i

Perpendicular to the sloping surface
`N=mgcostheta` .............ii
Balancing torque about point `P`,
`Fxxh=mgcosthetab/2` .................iii
when the block is on the verge of tipping, the normal reaction will pass through the edge of the block.
from eqn i, ii and iii
`F=mgsintheta-mumg cos theta`........iv
On substiting `F` in eqn ii we obtain
`(mgsintheta-mumgcostheta)h-mgcosthetah/2=0`
Which on solving for `h//b` yields `h/b= 1/((2mu_(2)-tantheta))`