Question

If a body floats with (m/n)th of its volume above the surface of water, the relative density of the material of the body is

• A. $(n-m)/n$
• B. $m/n$
• C. $n/m$
• D. $(n-m)/m$

Answer 1

The correct option is A $(n-m)/n$

Let the density of the body be $\rho$ and the density of water be ${\rho }_w$ and the volume of body be $V$.

Relative density of the body = $\frac{\rho }{{\rho }_w}$

The body floats with $\frac{m}{n}$ th of its volume above water .

Fraction of volume submerged in water = $(1-\frac{m}{n})$

Volume of water displaced = $(1-\frac{m}{n})$ $V$

Applying Archimedes' principle :

$\rho Vg={\rho }_w(1-\frac{m}{n})Vg$

$\frac{\rho }{{\rho }_w}$ = $(1-\frac{m}{n})$

$\frac{\rho }{{\rho }_w}$ = $\left(\frac{n-m}{n}\right)$

Hence , relative density of the material of the body is $\left(\frac{n-m}{n}\right)$ .