Question

Two bodies A and B are floating in water in such a way that $\frac{9}{10}$ volume of A and $\frac{2}{3}$ volume of B are submerged under water. The ratio of the densities of A and B is-

• A. $3:5$
• B. $5:3$
• C. $20:27$
• D. $27:20$

Answer 1

The correct option is D $27:20$

According to the question

In the above figure.

where $l_w$ is the density of water and ${\sigma }_{a}and{v}_B$

represent the density and volume of $B$.

Hence, conserving force for $A$

$\begin{array}{c}{\sigma }_a{v}_{a}g=l_{w}9v_{a}g\\ {\sigma }_a=\frac{l_{w}9}{10}\\ ForB\\ {\sigma }_b{v}_{b}g=l_w\frac{2}{3}{v}_{b}g\\ {\sigma }_b=\frac{2}{3}{l}_w\\ RatioofdesitiesofAandBis=\frac{{\sigma }_a}{{\sigma }_b}=\frac{\frac{l_{w}9}{10}}{\frac{2}{3}{l}_w}=\frac{27}{20}=27:20\\ Hence,theoptionDistherequiredanswer.\end{array}$