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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

ρKP

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B

KρP

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C

PKρ

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D

ρPK

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Solution

The correct option is D

ρPK


Step 1: Given data

The density of material = ρ

Bulk Modulus of elasticity = K

Pressure applied on material = P

Step 2: Formula used

The following formula is used to compute the density:

densityρ=massMvolumeV·····1ρ=mV2V(whenthemassisconstant)

The general formula of the bulk modulus of elasticity is:

K=-PVVVV=-PK······2

Where K=Bulk modulus, P=Pressure, V=Change in volume and V=Initial volume

Step 3: Compute increase in density

If the mass remains constant in equation 1 then it gives,

ρρ=-VVVV=-ρρ·····3

Equate equation 3 and equation 2,

-ρρ=-PKρ=ρPK

Thus, the magnitude of increase in density of the material will be ρPK.

Hence, option D is the correct answer.


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