Question

Two metals of relative densities 10 and 20 are taken and two alloys are prepared from the given metals. The first alloy contains equal masses of the two given metals. The other alloy contains equal volumes of the two given metals. Two cubes are made out of these two alloys, then find the ratio of the densities of the two cubes.

Answer 1

$R.D_A=10\Rightarrow d_A=10gc{m}^{-3}=\frac{m_1}{V_1}$
$R.D_B=20\Rightarrow d_B=20gc{m}^{-3}=\frac{m_2}{V_2}$

Let the mass of each metal be m and their respective volumes by $V_1$ and $V_2$
$\therefore p_{1^{st}}=\frac{2m}{V_1+V_2}=\frac{2m}{\frac{m}{10}+\frac{m}{20}}=\frac{40}{3}$

$p_{2^{nd}alloy}=\frac{m_1+m_2}{2V}=\frac{10V+20V}{2V}=15$

On preparation of cubes out of two alloys density remains same.
$\frac{p_{1^{st}}cube}{p_{2^{nd}}cube}=\frac{p_{1^{st}}alloy}{p_{2^{nd}}alloy}=\frac{40}{3\times 15}=\frac{8}{9}$