Question

A block of wood floats in water with $(4/5{)}^{th}$ of its volume submerged. In an oil, it floats with $(9/10{)}^{th}$ of its volume submerged. The ratio of the density of oil and water is:

• A. $8/9$
• B. $9/8$
• C. $19/25$
• D. $25/18$

Answer 1

Answer: (B)

$9/8$

Let the density of wood be $a$.

For floating in water,
${\rho }_{b}vg=\frac{4}{5}v\times d_w\times g$ .............1

For floating in oil,
${\rho }_{b}vg$ = $\frac{9}{10}v\times d_{oil}\times g$ .........2

Dividing 2 from 1 we get:
$\frac{d_{oil}}{d_w}=\frac{9}{10}\times \frac{5}{4}$

$\frac{d_{oil}}{d_w}=\frac{9}{8}$