Question

A solid block of silver with density $10.5\times 10^{3}kg{m}^{-3}$ is subjected to an external pressure of $10^{7}N{m}^{-2}$. If the bulk modulus of silver is $17\times 10^{10}N{m}^{-2}$, 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, $V^{\prime }=V-\Delta V$
$=V-\frac{V\Delta p}{K}=V(11-\Delta p/K)$
or $\frac{m}{{\rho }^{\prime }}=\frac{m}{\rho }\left(1-\frac{\Delta p}{K}\right)$
or ${\rho }^{\prime }=\frac{\rho }{\left(1-\frac{\Delta p}{K}\right)}$
or $\rho =\frac{10.5\times 10^3}{\left(1-10^7/17\times 10^{10}\right)}=0.61kg{m}^{-3}$