A body floats in water with 40 % of its volum | vedclass

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Question

(C) For a body floating in a liquid, the weight of the body equals the weight of the displaced liquid. Let $V$ be the total volume of the body and $d$

Vedclass · Accepted Answer

$1.5$

Vedclass · Answer

(C) For a body floating in a liquid, the weight of the body equals the weight of the displaced liquid. Let $V$ be the total volume of the body and $d$ be its density.Case $1$: Floating in water (density $ho_w = 1 	ext{ g/cm}^3$)Volume immersed $V_{in} = V - 0.4V = 0.6V$.Weight of body = Weight of displaced water$V \cdot d \cdot g = (0.6V) \cdot ho_w \cdot g$$d = 0.6 \cdot 1 = 0.6 	ext{ g/cm}^3$.Case $2$: Floating in oil (density $ho_{oil}$)Volume immersed $V_{in} = V - 0.6V = 0.4V$.Weight of body = Weight of displaced oil$V \cdot d \cdot g = (0.4V) \cdot ho_{oil} \cdot g$$0.6 = 0.4 \cdot ho_{oil}$$ho_{oil} = \frac{0.6}{0.4} = 1.5$.Thus, the relative density of the oil is $1.5$.

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

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