Question

An alloy of gold and copper weighs $0.2kg$ in air and $0.188kg$ in water. The densities of gold and copper are $19.3\times {10}^{3}kg{m}^{-3}$ and $8.93\times {10}^{3}kg{m}^{-3}$respectively. The amount of gold in block is nearly:

• A. $12\times {10}^{-3}kg$
• B. $17\times {10}^{-3}kg$
• C. $0.173kg$
• D. $0.388kg$

Answer 1

Answer: (C)

$0.173kg$

In air weight of block is
$V_1{\rho }_{1}g+V_2{\rho }_{2}g=0.2kg$
$V_1=$ Volume of gold .
$V_2=$ Volume of copper .
In water appareng weight is
$V_1({\rho }_1-\rho )g+V_2({\rho }_2-\rho )g=0.188.$
Solving both equations
$\Rightarrow V_1=9\times {10}^{-3}$
$\therefore amountofgold=V_1{\rho }_1=9\times {10}^{-3}\times 19.3\times {10}^{-3}$
$=0.173kg.$