Question

For a constant hydraulic stress on an object, the fractional change in the object volume $(\frac{\triangle V}{V})$ and its bulk modulus (B) are related as
(a) $\frac{\triangle V}{V}\propto B$
(b) $\frac{\triangle V}{V}\propto\frac{1}{B}$
(c) $\frac{\triangle V}{V}\propto B^{2}$
(d) $\frac{\triangle V}{V}\propto B^{-2}$

Answer 1

the option is d I don't know correctly

Answer 2

Answer:

B) ∆V/V ∝ 1/B

Explanation:

Volume of the object = (∆V/V) ( Given)

Bulk modulus is defined as the ratio of pressure and the volume strain.

= Bulk modulus = B = pressure/volume strain

Thus, volumetric strain = change in volume /original volume

Hence, if change in volume is ∆VA and the original volume is V -

Volumetric strain = ∆V/V

B = P/∆V/V

Therefore, B ∝ 1/{∆V/V}

= ∆V/V ∝ 1/B

Thus, the bulk modulus are related as - ∆V/V ∝ 1/B.