Question

A body floats in water with $40$% of its volume outside water. When the same body floats in an oil $60$% of its volume remains outside oil. The relative density of oil is:

• A. $0.9$
• B. $1.0$
• C. $1.2$
• D. $1.5$

Answer 1

The correct option is D $1.5$

Let $V$ and $d$ be the volume and density of body respectively.

Body immersed in water:

Volume of body outside the water is $0.4V$

Volume of body inside the water, $V_1=0.6V$

Let the density of water be $d_w$

Using Archimedes principle, $Vdg=V_1{d}_{w}g$

$\therefore$ $Vdg=\left(0.6V\right)d_{w}g$ ...........(1)

Body immersed in oil :

Volume of body outside the oil is $0.6V$

Volume of body inside the oil, $V_2=0.4V$

Let the density of oil be $d_o$

Using Archimedes principle, $Vdg=V_2{d}_{o}g$

$\therefore$ $Vdg=\left(0.4V\right)d_{o}g$ ...........(2)

From (1) and (2), $0.6d_{w}g=0.4d_{o}g$

$⟹$$\frac{d_o}{d_w}=\frac{0.6}{0.4}=1.5$