Question

A body floats in water with 70% of the volume inside the water. When the same body floats on another liquid, it floats with 60% of the volume outside the liquid. The relative density of the liquid is (a) 1 (b) 1.75 (c) 0.9 (d) 1.16 ​

Answer 1

Answer: (b) 1.75

Explanation:

Let us consider the density of water to be x, and density of the other liquid to be y. Let m and v be the mass and volume of body

Since 70% of the volume of body is inside when floating on water,

$x=\frac{m}{\frac{70}{100}v}=\frac{10m}{7v}$

and since 60% of the volume of body is outside when floating on other liquid,

$y=\frac{m}{(1-\frac{60}{100})v}=\frac{m}{\frac{2}{5}v}=\frac{5m}{2v}$

Relative density of liquid = Density of liquid/Density of water = y/x

$\frac{y}{x}=\frac{\frac{5m}{2v}}{\frac{10m}{7v}}=\frac{5m\times7v}{2v\times10m}=\frac{7}{4}$
$=1.75$

Hope it helped