A body of density ρ  is dropped ρ is dropped from rest from a height ‘h’ into a lake of density σ where σ>ρ neglecting all dissipative forces. The maximum depth to which the body sinks before returning to float on surface

Velocity of the ball as it reaches water surface v=2gh Net upward force acting on the bodyF=ρvg−ρ'vg⇒ma=ρvg−ρ'vg⇒(ρ'v)a=vg(ρ−ρ')⇒a=g(ρ−ρ'ρ')Let's say it sinks to depth h' , at this instant final velocity becomes v=0, So, we havev2−u2=2as⇒(2gh)2=2g(ρ−ρ'ρ')h'⇒h1=hρ'ρ−ρ'  (∵ρ=σ) (∵ρ'=ρ)∴h1=hρσ−ρ