Question

If a pressure of $8\times 10^{8}N\cdot m^{-2}$ is applied to a lead block so that its volume reduces by $20\%$. The Bulk modulus of lead block is______

• A. $4\times 10^{7}N\cdot m^{-2}$
• B. $4\times 10^{8}N\cdot m^{-2}$
• C. $4\times 10^{9}N\cdot m^{-2}$
• D. $4\times 10^{10}N\cdot m^{-2}$

Answer 1

Answer: (C)

Pressure applied on the block,
$p=8\times 10^{8}N{m}^{-2}$
If $V_1$ be initial volume, then final volume of block,
$V_2=V_1-20\%$ of $V_1=V_1-\frac{20}{100}{V}_1$
$V_2=\frac{4}{5}{V}_1$
$\therefore$ Change in volume,
$\Delta V=V_1-V_2=V_1-\frac{4}{5}{V}_1$
$\Rightarrow =\frac{V_1}{5}$
$\therefore$ Bulk modulus,
$B=\frac{p}{\Delta V/V}=\frac{pV}{\Delta V}$
$=\frac{8\times 10^8\times V_1}{V_1/5}$
$=4\times 10^{9}N{m}^{-2}$