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 :

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:

  • Elasticity: When an object is stretched, it changes its shape and when we leave, it retrieves its shape. Or we can say it is the property of retrieving the original shape once the external force is removed. For example Spring
  • 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.
  • Ductility: When an object is been pulled in thin sheets, wires or plates, it will be assumed that it has ductile properties. It is the property of drawing into thin wires/sheets/plates. For example Gold or Silver
  • Strength: The ability to hold out applied stress without failure. Many types of objects have higher strength than others.