HYDROSTATICS. Sol 



circular boundary just out of the fluid, and the lower one 

 completely immersed : prove that the length of the axis : radius 

 :: 7:4.' 



15G7. If a circular lamina be in a vertical position with its 

 centre at a depth c below the surface of a heavy uniform fluid, 

 the depth of the centre of pressure below the centre of figure is 



r- , a being the radius and c > a. 

 4c 



1568. A cone of density p floats with a generator vertical in 

 a fluid of density <r, the base being out of the fluid; prove that, 

 2a being the vertical angle, 



and that the length of the vertical side immersed is to the length 

 of the axis as cos 2a : cos a. 



1 "G9. A right cone is moveable about its vertex which is 

 fixed at a given distance c below the surface of a heavy fluid, and 

 rests with its axis h inclined at an angle to the vertical, its base 

 being completely out of the fluid : prove that 



OOS0 cog* a _ <rh* f 

 (cos'fl-sin'a)*"^' 



2a being the vertical angle, p, a- the densities of the fluid ;u:<i 

 respectively. Prove that this position is .- ut cannot exist 



unless <rh* cos'a > pc 4 . 



1570. An elliptic tiitx* half full of hruvy inoompmiUi fluid 

 revolves about a fixed vertical axis in its plane with angulai 

 city <o: prove that the angle which i iit lim> j>inmg the 



free surfaces of the fluid makes with the vertical will be 



ng the distance of the axis from the centre of the ellipse. 



