For a floating body of volume V, the relation between the volume of its submerged part $v$, the densities of liquid (ρ_L) and the body (ρ_S) is :

1. $\dfrac{v}{V}$ = $\dfrac{ρ$s}{ρL}

2. $\dfrac{V}{v}$ = $\dfrac{ρ$s}{ρL}

3. $v \times ρ$s = V \times ρL

4. none of these

$\dfrac{v}{V}$ = $\dfrac{ρ$s}{ρL}

Reason —

Given,

Volume of body = V

Volume of body submerged in liquid = v

Density of body = ρ_s

Density of liquid = ρ_L

Let weight of the body be W. W = volume of the body x density of the body x g = V ρ_s g

Weight of liquid displaced by the body will be equal to upthrust. Let it be F_B.

F_B = volume of the liquid displaced x density of the liquid x g = v ρ_L g

From principle of floatation,

W = F_B

⇒ V ρ_s g = v ρ_L g

⇒ $\dfrac{v}{V}$ = $\dfrac{ρ$s}{ρL}

Hence proved.