Question

A solid block of silver with density $10.5 \times 10^{3} kg m ^{-3}$ is subjected to an external pressure of $10^{7} Nm ^{-2}$. If the bulk modulus of silver is $17 \times 10^{10} Nm ^{-2}$, the change in density of silver (in $kg m ^{-3}$ ) is

• A. 0.61
• B. 1.7
• C. 6.1
• D. $17 \times 10^{3}$

Answer 1

Answer: (A)

Decrease in volume, $\Delta V=\frac{\Delta p \times V}{K}$
Final volume, $V'=V-\Delta V$
$=V-\frac{V \Delta p}{K}=V(11-\Delta p / K)$
or $\frac{m}{\rho^{\prime}}=\frac{m}{\rho}\left(1-\frac{\Delta p}{K}\right)$
or $ \rho'=\frac{\rho}{\left(1-\frac{\Delta p}{K}\right)} $
or $\rho =\frac{10.5 \times 10^{3}}{\left(1-10^{7} / 17 \times 10^{10}\right)}=0.61 \,kg m ^{-3} $