Question

The fraction of a floating object of volume $V_o$ and density $d_o$ above the surface of a liquid of density d will be :

• A. $\frac{d_o}{d}$
• B. $\frac{d{d}_o}{d+d_o}$
• C. $\frac{d-d_o}{d}$
• D. $\frac{d{d}_o}{d.d_o}$

Answer 1

Answer: (C)

$\frac{d-d_o}{d}$

Let the volume above the surface be $V$.

So volume of submerged part is, $V_0-V$

Let buoyancy force balance the gravitational force. So,

$(V_0-V)dg=V_0{d}_{0}g⟹V_0(d-d_0)=Vd$

$⟹V/V_0=(d-d_0)/d$