For a constant hydraulic stress on an object, the fractional change in the object's volume (Δ V / V) and its bulk modulus (B) are related as :

Question

For a constant hydraulic stress on an object, the fractional change in the object's volume (Δ V / V) and its bulk modulus (B) are related as : (A) (Δ V/V) propto B (B) (Δ V/V) propto (1/B) (C) (Δ V/V) propto B2 (D) (Δ V/V) propto B-2

Tardigrade Admin · Accepted Answer

When strain is small the ratio of the normal stress to the volume strain is called the bulk modulus of the material of the body.

B = \frac{normal stress}{volume strain}

B = - \frac{Δ P}{Δ V / V}

B \propto \frac{1}{\frac{Δ V}{V}}

\Rightarrow \frac{Δ V}{V} \propto \frac{1}{B}

Q. For a constant hydraulic stress on an object, the fractional change in the object's volume $(Δ V / V)$ and its bulk modulus $(B)$ are related as :

$\frac{Δ V}{V} \propto B$

$\frac{Δ V}{V} \propto \frac{1}{B}$

$\frac{Δ V}{V} \propto B^{2}$

$\frac{Δ V}{V} \propto B^{- 2}$

When strain is small the ratio of the normal stress to the volume strain is called the bulk modulus of the material of the body.
$B = \frac{normal stress}{volume strain}$
$B = - \frac{Δ P}{Δ V / V}$
$B \propto \frac{1}{\frac{Δ V}{V}}$
$\Rightarrow \frac{Δ V}{V} \propto \frac{1}{B}$

Q. For a constant hydraulic stress on an object, the fractional change in the object's volume (ΔV/V) and its bulk modulus (B) are related as :

VΔV​∝B

VΔV​∝B1​

VΔV​∝B2

VΔV​∝B−2

When strain is small the ratio of the normal stress to the volume strain is called the bulk modulus of the material of the body. B= volume strain normal stress ​ B=−ΔV/VΔP​ B∝VΔV​1​ ⇒VΔV​∝B1​