a cubical block of mass M is kept inside a liquid of variable density d = do (1+by) where y = distance from upper surface. initially (1/4)^th of cubical block is immersed. the mass M' of the additional block to immerse it just completely is..

(do and b are constants, side of cube = l )

 

Let boyant force in first case be B1 and in second case is B2

 

B1 = l²*do*g_{[0 ]}^{[l/4 ]} (1+by)dy

 

B2 = l²*do*g_{[0 ]}^{[l ]} (1+by)dy

 

M' = (B2-B1)/g =l²*do*(3l/4+(b/2)*15*l^2/16)