Question

A solid body floating in water has $\frac{1}{6^{th}}$ of the volume above surface.What fraction of its volume will project upwards if it floats in a liquid of specific gravity $1.2$?

• A. $\frac{29}{200}$
• B. $\frac{11}{36}$
• C. $\frac{19}{200}$
• D. $\frac{9}{100}$

Answer 1

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

Volume inside water $=\frac{5V}{6}$

so

${\rho }_{s}vg={\rho }_{\omega }\frac{5v}{6}\times g$

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

Now

$\frac{{\rho }_s}{{\rho }_w}\times v\times g=1\cdot 2v_{i}g$

$\frac{v_i}{v}=\frac{50}{72}=\frac{25}{36}$

$\text{Fraction above liquid}=\frac{11}{36}$

Answer:- $\frac{11}{36}$