(a). A body may sink in one liquid but float on another. Given examples.
(b). It is easier to swi in sea water than in a river water. Why ?
(c). A hollow ball has an internal diameter of 10 cm and external diameter of 12 cm. it is found that it floats on water. Find the density of the material of the ball (The volume of a sphere varies as the cube of the diameter).

Explanation

(a). (i) A lump of iron sinks in water but floats on mercury as `rho_("iron")gtrho_("water")` and `rho_("iron")ltrho_("mercury")`
(ii). A fresh egg sinks in ordinary water but floats on strong saline as `rho_("saline")gtrho_("water")(rho_(egg)gtrho_("water")` but `rho_(egg)ltrho_("saline")`).
(b). `rho_("sea water")gtrho_("river water")`
(c). As `Vpropd^(3),V=kd^(3),V_(ext)=k(12cm)^(3),V_("int")=k(10cm)^(3)`
volume of the material of the ball, `V=V_(ext)-V_("int")=k[12^(3)-10^(3)]cm^(3)=(728k)cm^(3)`
mass of the ball, `m=Vrho=(728rho)g` (where `rho` is density of the material ball and `g//cm^(3)`) volume of water displaced `V_(ext)=(1728k)cm^(3)`
Mass of water displaced `m'=V_(ext)(1g//cm^(3))=(1728k)g`
from the principle of floatation `m'=m` or (1728k)`g=(728krho)g`
whence, `rho=((1728k)g)/((728k)g)=2.37g//cm^(3)`