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

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

Tardigrade Admin · Accepted Answer

Using the law of buoyancy, we have V σ g=0.6 V σ1 g, for the part of body outside oil and V σ g=0.4 V σ2 g, for the part of body outside water, hence we get 1=(0.6 σ1/0.4 σ2) So we have, (σ2/σ1)=(6/4)=(3/2) =1.5

Q. 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

$0.9$

$1.0$

$1.2$

$1.5$

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

Q. 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

0.9

1.0

1.2

1.5