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

Answer: (D)

$1.5$

Answer 2

Using the law of buoyancy, we have $V \sigma g=0.6\, V \sigma_{1} g$, for the part of body outside oil and $V \sigma g=0.4 \,V \sigma_{2} g$, for the part of body outside water, hence we get
$1=\frac{0.6 \sigma_{1}}{0.4 \sigma_{2}}$
So we have, $\frac{\sigma_{2}}{\sigma_{1}}=\frac{6}{4}=\frac{3}{2}$
$=1.5$