Question:
For a constant hydraulic stress on an object, the fractional change in the object's volume $(\Delta V / V)$ and its bulk modulus $(B)$ are related as :
For a constant hydraulic stress on an object, the fractional change in the object's volume $(\Delta V / V)$ and its bulk modulus $(B)$ are related as :
Updated On: Apr 7, 2024
- $\frac{\Delta V}{V} \propto B$
- $\frac{\Delta V}{V} \propto \frac{1}{B}$
- $\frac{\Delta V}{V} \propto B^2$
- $\frac{\Delta V}{V} \propto B^{-2}$
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The Correct Option is B
Solution and Explanation
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.
$B =\frac{\text { normal stress }}{\text { volume strain }}$
$B =-\frac{\Delta P}{\Delta V / V}$
$B \propto \frac{1}{\frac{\Delta V}{V}}$
$\Rightarrow \frac{\Delta V}{V} \propto \frac{1}{B}$
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Concepts Used:
Mechanical Properties of Solids
Mechanical properties of solids intricate the characteristics such as the resistance to deformation and their strength. Strength is the ability of an object to resist the applied stress, to what extent can it bear the stress.
Therefore, some of the mechanical properties of solids involve:
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- Plasticity: When an object changes its shape and never attains its original shape even when an external force is removed. It is the permanent deformation property. For example Plastic materials.
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