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Q.

The density of a metal at normal pressure is $ρ$ . Its density when it is subjected to an excess pressure $P$ is $ρ'$ . If B is the bulk modulus of the metal, the ratio $\frac{ρ'}{ρ}$ is

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a

$\frac{1}{1 - \frac{ρ}{B}}$

b

$1 + \frac{B}{ρ}$

c

$\frac{1}{1 - \frac{B}{ρ}}$

d

$1 + \frac{ρ}{B}$

answer is A.

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Detailed Solution

Density, $ρ = \frac{m}{V}$ or $ρ \propto \frac{1}{V}$ (as $m =$ constant)

$∴ \frac{ρ'}{ρ} = \frac{V}{V'} = \frac{V}{V + d V}$ (as $B = - \frac{p}{d V / V}$ )

$∴ \frac{ρ'}{ρ} = \frac{V}{V - \frac{V P}{B}} = \frac{1}{1 - \frac{P}{B}}$ .

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The density of a metal at normal pressure isρ . Its density when it is subjected to an excess pressure P is ρ' . If B is the bulk modulus of the metal, the ratio ρ'ρ is