Question

Two bodies $A$ and $B$ are having the same mass $M$. While the volume of body $A$ is lesser than volume of body $B$. What is the relation between density of body $A$ and body $B$.
(Take density of body $A={\rho }_A$ and density of body $B={\rho }_b$ & volume of body $A=V_A$ and density of body $B=V_B$ )

Answer 1

Given: mass of body $A$ and body $B=M$
We know that,
$\rho =\frac{M}{V}$
If both A and B are having the same mass, then density will only be dependent on volume.
$\rho \propto \frac{1}{V}$
Density is directly proporsional to $\frac{1}{V}$. Body $A$ have a lesser volume comparatively body $B$. Then ${\rho }_A$ will be greater than ${\rho }_B$