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Question

(B) The bulk modulus $(B)$ is defined as the ratio of hydraulic stress $(\Delta p)$ to the volumetric strain $\left( \frac{\Delta V}{V} \right)$.Mathe

Vedclass · Accepted Answer

$\frac{\Delta V}{V} \propto \frac{1}{B}$

Vedclass · Answer

(B) The bulk modulus $(B)$ is defined as the ratio of hydraulic stress $(\Delta p)$ to the volumetric strain $\left( \frac{\Delta V}{V} \right)$.Mathematically,$B = \frac{\Delta p}{\Delta V/V}$.Rearranging this formula,we get $\frac{\Delta V}{V} = \frac{\Delta p}{B}$.Since the hydraulic stress $(\Delta p)$ is given as a constant,we have $\frac{\Delta V}{V} \propto \frac{1}{B}$.Therefore,the fractional change in volume is inversely proportional to the bulk modulus.

For a constant hydraulic stress on an object,the fractional change in the object's volume $\left( \frac{\Delta V}{V} \right)$ and its bulk modulus $(B)$ are related as

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