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JEE Main 202126 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
26 February
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2021 · 26 February · Morning Shift · Physics · Mechanical Properties of Solids

The normal density of a material is ρ and its bulk modulus of...

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

Options

  1. APKρ\dfrac{PK}{ρ}
  2. BρPK\dfrac{ρP}{K}
  3. CρKP\dfrac{ρK}{P}
  4. DKρP\dfrac{K}{ρP}

Correct answer

B. ρPK\dfrac{ρP}{K}

Step-by-step solution

ρ=MVρ = \dfrac{M}{V}

dρρ=−dVV\dfrac{dρ}{ρ} = - \dfrac{dV}{V}

k=−PdVVk = - \dfrac{P}{\dfrac{dV}{V}}

−dVV=Pk- \dfrac{dV}{V} = \dfrac{P}{k}

dρρ=Pk⇒dρ=ρPk\dfrac{dρ}{ρ} = \dfrac{P}{k} ⇒ dρ = \dfrac{ρP}{k}

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