The normal density of a material its $ρ$ 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

Option 1 - <math> <mrow> <mfrac> <mrow> <mi>K</mi> </mrow> <mrow> <mi>ρ</mi> <mi>P</mi> </mrow> </mfrac> </mrow> </math>

Option 2 - <math> <mrow> <mfrac> <mrow> <mi>P</mi> <mi>K</mi> </mrow> <mrow> <mi>ρ</mi> </mrow> </mfrac> </mrow> </math>

Option 3 - <math> <mrow> <mfrac> <mrow> <mi>ρ</mi> <mi>K</mi> </mrow> <mrow> <mi>P</mi> </mrow> </mfrac> </mrow> </math>

Option 4 - <math> <mrow> <mfrac> <mrow> <mi>ρ</mi> <mi>P</mi> </mrow> <mrow> <mi>K</mi> </mrow> </mfrac> </mrow> </math>

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Payal Gupta | Contributor-Level 10

7 months ago

Correct Option - 4

Detailed Solution:

From defined of bulk modulus

$K = - \frac{P}{(d V / V)} . . . . . . . (1)$

m = $ρ v = c o n s t a n t$

$ρ d V + V d ρ = 0$

$\frac{d V}{V} = - \frac{d ρ}{ρ} . . . . . . . . . (2)$

With the help of equations (1) and (2), we can write

$K = - \frac{P}{(- \frac{d ρ}{ρ})} = \frac{ρ P}{d ρ} \Rightarrow d ρ = \frac{ρ P}{K}$

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Physics Mechanical Properties of Solids 2025

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The normal density of a material its 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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