Question

An alloy made of two metals $Au$ and $Cu$ weighs $200gwt$ in air and $160gwt$ in water. If densities of metals $Au$ and $Cu$ are $20gc{m}^{-3}$ and $4gc{m}^{-3}$, then find the percentage of mass of each metal present

Answer 1

Let the volume of Au be $V_{Au}$ and of Cu be $V_{CU}$

Let the density of Au be ${\rho }_{Au}$ and of Cu be ${\rho }_{CU}$

For air

$V_{Au}{\rho }_{Au}g+V_{Cu}{\rho }_{Cu}g=200gwt$

$V_{Au}\times 20+V_{Cu}\times 4=200$ .....(1)

In water it will feel buoyancy force

$(V_{Au}{\rho }_{Au}+V_{Cu}{\rho }_{Cu})-(V_{Au}+V_{Cu}){\rho }_{water}g=160gwt$

we know that ${\rho }_{water}=1$

$V_{Au}\times 20+V_{Cu}\times 4-(V_{Au}+V_{Cu})=160$ ......(2)

using equation 1 in 2

$V_{Au}=2.5c{m}^3$

$V_{Cu}=37.5c{m}^3$

mass of Au is $m_{Au}=2.5\times 20=50gm$

mass of Cu is $m_{Cu}=37.5\times 4=150gm$

Percentage mass of Au is $\frac{50\times 100}{200}=25$%

mass of cu is $75$%