When a loaded cargo ship enters a river from the sea, it sinks by a length x. When the ship is totallly unloaded, it rises by a length y. When the unloaded ship again enters the sea, it rises by z cm more. If the density of water of the river is rho_(w) and the body of the ship is vertical, show that the density of sea water is (yrho_(w))/((z-x+y)).

When a loaded cargo ship enters a river from the sea, it sinks by a le

1.	When a loaded cargo ship enters a river from the sea, it sinks by a length x. When the ship is totallly unloaded, it rises by a length y. When the unloaded ship again enters the sea, it rises by z cm more. If the density of water of the river is rho_(w) and the body of the ship is vertical, show that the density of sea water is (yrho_(w))/((z-x+y)).
Answer» Solution :Let the WEIGHT of the loaded ship be w , the weight of cargo be w. , the base-area of the ship be A and the DENSITY of sea water be `rho`. Let US ALSO assume that the loaded ship sinks a LENGTH h in sea water. `therefore` In the case of floatation in sea water, `w=Ahrho""...(1)` In the case of floatation in river water, `w=A(h+x)rho_(w)""...(2)` When the ship is unloaded, `w-w.=A(h+x-y)rho_(w)""...(3)` When the unloaded ship enters the sea, `w-w.=A(h+x-y-z)rho""...(4)` From (1) and (2), we get `Ahrho=A(h+x)rho_(w)or,h+x=(hrho)/rho_(w)` From (3) and (4), we get `A(h+x-y)rho_(w)=A(h+x-y-z)rho` or, `h+x-y=(h+x-y-z)rho/rho_(w)` or, `(hrho)/rho_(w)-y=(hrho)/rho_(w)+(x-y-z)rho/rho_(w)or,y=(y+z-x)rho/rho_(w)` or, `rho=(yrho_(w))/((z-x+y))`.