First slide

Elastic Modulie

Question

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, then the ratio $ρ$ '/ $ρ$ is

Moderate

A

$1 + P / B$
B

$1 + B / P$
C

$\frac{1}{(1 - B / P)}$
D

$\frac{1}{(1 - P / B)}$

Solution

Magnitude of bulk modulus,
$B = \frac{P}{d V / V} or d V = \frac{P V}{B}$
$∴ ρ^{'} = \frac{M}{V - d V} = \frac{M}{V - (P V / B)}$
$= \frac{M}{V (1 - P / B)} = \frac{ρ}{(1 - P / B)} (∵ ρ = \frac{M}{V})$
$∴ \frac{ρ^{'}}{ρ} = \frac{1}{(1 - P / B)}$

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