Question

A piece of brass (alloy of copper and zinc) weighs 12.9 g in air. When completely immersed in water it weighs 11.3 g. What is the mass of copper contained in the alloy ? (Specific gravities of copper and zinc are 8.9 and 7.1 respectively)

• A. 7.61 g
• B. 8.61 g
• C. 9.61 g
• D. 10.61 g

Answer 1

Answer: (A)

Let the alloy contains m g of copper, the amount of zinc will be $(12.9-m)g$. Therefore, the volumes of copper and zinc will be respectively ,
$V_{Cu=\frac{m}{{\rho }_{Cu}}}$ and $V_{Zn}=\frac{\left(12.9-m\right)}{{\rho }_{Zn}}\left[as\rho =\frac{m}{V}\right]$
The total volume of alloy,
$V=V_{Cu}+V_{Zn}=\frac{m}{8.9}+\frac{(12.9-m)}{7.1}$ ....(i)
Now as the weight of alloy in air and water is 12.9 g and 11.3 g respectively,
$\therefore$ Upthrust = $V\sigma g$ = loss in weight = (12.9 - 11.3) g
or $V$ = 1.6 cc ...(ii)
[where density of water is $\sigma$ = 1 g/cc]
Substituting $V$ from equation (ii) in (i) and solving for $m$, we get $m$ = 7.61 g