Question

An alloy contains two metals X and y of densities 4x10^3 and 6x10^3. Find the densities of the alloy given that the volume of X is thrice the volume of Y.

Answer 1

$$m_x=\rho_x V_x=3\rho_x V_y$$

$$m_y=\rho_y V_y$$

The density of the alloy is

$$\rho=\frac{m_x+m_y}{V_x+V_y}=\frac{3\rho_x V_y+\rho_y V_y}{3V_y+V_y}$$

$$\rho=\frac{3\rho_x +\rho_y }{4}=\frac{3(4000) +6000 }{4}$$

$$\rho=4500\frac{kg}{m^3}$$