when the container moves down on the inclined plane, acceleration of the container is ( g sinθ ) .
Since the container is accelerated downwards, backside of liquid level is greater than front side of liquid level.
pressure difference between backside and frontside ≈ ρ g ( h1 - h2 ) cosθ ............(1)
If this pressure difference given above is due to acceleration, then we get, ρ g ( h1 - h2 ) cosθ = ( ρ L g sinθ ) ..............(2)
Hence from eqn.(2), slope of the free surface, [ ( h1 - h2 )/L ] = tanθ