Question

The bulk modulus of a metal is $8\times 10^{9}N{m}^{-2}$ and its density is $11gc{m}^{-2}$. The density of this metal under a pressure of $20,000Nc{m}^{-2}$ will be (in $gc{m}^{-3}$ )

• A. $\frac{440}{39}$
• B. $\frac{431}{39}$
• C. $\frac{451}{39}$
• D. $\frac{40}{39}$

Answer 1

Answer: (A)

Here, $p=20,000Nc{m}^{-2}=2\times 10^{8}N{m}^{-2}$
As, $k=\frac{pV}{\Delta V}$
or $\Delta V=\frac{pV}{k}$
$=\frac{2\times 10^8\times V}{8\times 10^9}=\frac{V}{40}$
New volume of the metal,
$V^{\prime }=V-\Delta V=V-\frac{V}{40}=\frac{39V}{40}$
New mass of the metal
$=V^{\prime }\times \rho =\frac{39V}{40}{\rho }^{\prime }=V\times 11$
or ${\rho }^{\prime }=\frac{40\times 11}{39}=\frac{440}{39}gc{m}^{-3}$