Question

A body floats with $\frac{5}{6}th$ of its total volume inside the water. When it floats in a liquid having relative density $1.2$, the fraction of its volume outside the liquid will be:

• A. $\frac{5}{11}$
• B. $\frac{7}{11}$
• C. $\frac{11}{24}$
• D. $\frac{11}{36}$

Answer 1

The correct option is D $\frac{11}{36}$

Given : Body floats in water with $\frac{5}{6}th$ volume inside water when it floats in a liquid of density $1.2$

To find : Fraction of volume inside liquid = ?

Solution: Case I: Floating in water.

Weight of Body = Buoyant force.

${\rho }_{B}Vg={\rho }_w\times \frac{5}{6}V\times g$

${\rho }_B=\frac{5}{6}{\rho }_w$

Case II: Floating In liquid

Weight of Body = Buoyant force In Liquid

${\rho }_B.Vg={\rho }_l{V}^{\prime }\times g$

$\frac{5}{6}{\rho }_w\times V\times g=1.2{\rho }_w{V}^{\prime }\times g$

$V^{\prime }=\frac{5}{6\times 1.2}V$

$V^{\prime }=\frac{5}{6}\times \frac{10}{12}V=\frac{25}{36}V$ $\to$ it is inside Liquid

Then fraction of volume outside Liquid

$V^{\prime }=V-\frac{25}{36}V$

$V^{\prime }=\frac{11}{36}V$