Question

What is the density of lead under a pressure of $2.0\times {10}^{8}N/m^2$ , if the bulk modulus of lead is $8.0\times {10}^{9}N/m^2$. Also, the initial density of lead is $11.4g/cm$${}^3$.

• A. $12.89g/c{m}^3$
• B. $14g/c{m}^3$
• C. $11.69g/c{m}^3$
• D. $Zero$

Answer 1

Answer: (C)

$11.69g/c{m}^3$

Using the definition of Bulk modulus we have
$K=\rho \frac{dP}{d\rho }$
or
${\rho }_2-{\rho }_1={\rho }_1\frac{dP}{K}$
or
${\rho }_2={\rho }_1(1+\frac{dP}{K})$
$=11.4(1+\frac{2\times {10}^8}{8\times {10}^9})$
$=11.69g/c{m}^3$