A solid body floating in water has `(1)/(5^(th))` of its volume immersed in it. What fraction of its volume will be immersed, if it floats in a liquid of specific gravity 1.2 ?

Explanation

Let volume of the solid-body = `V_(s)`
Density of the solid body = `rho_(s)`
Density of water = `rho_(w)`
Given that the body floats in water with one-fifth of its volume immersed i.e., immersed volume = `V_(s)/5`
`because rho_(s)/rho_(w) = ("Immersed volume of the body")/("Total volume of the body")`
`implies rho_(s)/rho_(w)= (V_(s)//5)/V_(s)`
`impliesrho_(s)/rho_(w) = 1/5`...(i)
Let `1/n^(th)` volume of the solid body is immersed when it floats in a liquid of relative density 1.2.
Density of liquid `rho_(l)=(1.2)rhp_(w)`
So, `rho_(s)/rho_(l) = (V_(s)ln)/V_(s)`
`implies 1/(1.2xx5) = 1/eta`
`implies 1/eta = 1/6`
Thus, one-sixth of the volume remains immersed.