JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Elasticity & SHM

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 :

(A) $\frac{K}{ρ P}$
(B) $\frac{P K}{ρ}$
(C) $\frac{ρ K}{P}$
(D) $\frac{ρ P}{K}$ ✓ Correct

Answer: (D)

Solution

Bulk modulus is defined as

K = - \frac{P}{Δ V / V}

. Since density

ρ = \frac{m}{V}

, we have

\frac{Δ ρ}{ρ} = - \frac{Δ V}{V}

. From the bulk modulus definition:

\frac{Δ V}{V} = - \frac{P}{K}

. Therefore,

\frac{Δ ρ}{ρ} = \frac{P}{K}

, which gives

Δ ρ = \frac{ρP}{K}

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option

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