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Physics Question on mechanical properties of solids

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

A

ΔVV∝B\frac{\Delta V}{V} \propto B

B

ΔVV∝1B\frac{\Delta V}{V} \propto \frac{1}{B}

C

ΔVV∝B2\frac{\Delta V}{V} \propto B^2

D

ΔVV∝B−2\frac{\Delta V}{V} \propto B^{-2}

Answer

ΔVV∝1B\frac{\Delta V}{V} \propto \frac{1}{B}

Explanation

Solution

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= normal stress  volume strain B =\frac{\text { normal stress }}{\text { volume strain }} B=−ΔPΔV/VB =-\frac{\Delta P}{\Delta V / V} B∝1ΔVVB \propto \frac{1}{\frac{\Delta V}{V}} ⇒ΔVV∝1B\Rightarrow \frac{\Delta V}{V} \propto \frac{1}{B}