6. Find the differential equation of the curves of equal pressure and density when a liquid is at rest under forces X,Y,Z per unit mass. 7. A solid cone is just immersed with a generating line in the surface; if 0 be the inclination to the vertical of the resultant pressure on the curved surface, prove that (1-3 sin a) tan 0 = 3 sin a cos a 2a being the vertical angle of the cone. 8. Find the condition of stability for a body floating in 9. a homogeneous liquid. A cylindrical piece of wood of length I and sectional area a is floating with its axis vertical in a cylindrical vessel of sectional area. A which contains water: prove that the work done is very slowly pressing down the wood until it is just completely immersed, is gal (1-)(-) Where p and denote the densities of the water and wood respectively.