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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:

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a

PKρ

b

ρKP

c

ρPK

d

KρP

answer is C.

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Detailed Solution

Mass = density × volume ⇒m=ρV⇒0=ρdV+Vdρ⇒dρ=−ρdVV Also, Bulk Modulus =K=−dPdVV⇒dVV=−dPK Thus, dρ=ρdPK here dP=P( given )⇒ Increase in density =dρ=ρPK

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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: