The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

Question

The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be : (A) (ρ K / P ) (B) (ρ P / K ) (C) ( K /ρ P ) (D) ( PK /ρ)

Tardigrade Admin · Accepted Answer

ρ=( M / V ) ( d ρ/ρ)=-( d V / V ) k =-( P /( d V ) V ) -( d V / V )=( P / k ) ( d ρ/ρ)=( P / k ) ⇒ d ρ=(ρ P / k )

Q. The normal density of a material is $ρ$ and its bulk modulus of elasticity is $K$ . The magnitude of increase in density of material, when a pressure $P$ is applied uniformly on all sides, will be :

$\frac{ρ K}{P}$

$\frac{ρP}{K}$

$\frac{K}{ρP}$

$\frac{P K}{ρ}$

$ρ = \frac{M}{V}$
$\frac{d ρ}{ρ} = - \frac{d V}{V}$
$k = - \frac{P}{\frac{d V}{V}}$
$- \frac{d V}{V} = \frac{P}{k}$
$\frac{d ρ}{ρ} = \frac{P}{k} \Rightarrow d ρ = \frac{ρP}{k}$

Q. The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

PρK​

KρP​

ρPK​