Question

Relative density of a body with respect to a medium of density ${\rho }_1$ is $a$. What is the relative density of the body with respect to a medium of density ${\rho }_2$?

• A. $\frac{a{\rho }_2}{{\rho }_1}$
• B. $\frac{a{\rho }_1}{{\rho }_2}$
• C. $\frac{{\rho }_1}{a{\rho }_2}$
• D. $\frac{{\rho }_2}{a{\rho }_1}$

Answer 1

The correct option is B $\frac{a{\rho }_1}{{\rho }_2}$

Relative density is defined as the ratio of density of substance to the density of any other substance.

$\therefore$ Relative density wrt to ${\rho }_1$, $a=\frac{\rho }{{\rho }_1}$ where $\rho$ is the density of substance.

$⟹$ $\rho =a{\rho }_1$

Thus relative density wrt to medium of density ${\rho }_2$, $a^{\prime }=\frac{\rho }{{\rho }_2}=\frac{a{\rho }_1}{{\rho }_2}$