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Find the density of material under a pressure $3\times 10^8N/m^2$ .Given the density of material $800Kg/m^3$.Bulk modulus of material $9\times 10^9N/m^2$.

$\begin{array}{1 1}(A)\;826Kg/m^3\\(B)\;774Kg/m^3\\(C)\;878Kg/m^3\\(D)\;\text{None of above}\end{array} $

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As density =$\large\frac{\text{mass}}{\text{volume}}$
$S=\large\frac{M}{V}$
$\large\frac{\Delta S}{S}=-\frac{\Delta V}{V}$
As pressure increase,volume decrease and density of material increases
We know $\large\frac{\Delta V}{V}=\frac{\rho}{B}$
$\Rightarrow \large\frac{3\times 10^8}{9\times 10^9}$
$\Rightarrow \large\frac{1}{3}$$\times 10^{-1}$
$\large\frac{\Delta S}{S}=\frac{1}{3}$$\times 10^{-1}$
$\Delta S=\large\frac{80}{3}$$=26.67Kg/m^3$
$S_{Final}=800+26.67$
$\Rightarrow 826.67Kg/m^3$
Hence (A) is the correct answer.
answered May 8, 2014 by sreemathi.v
 

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