Question

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 are related as
A) \frac{\Delta V}{V}\propto B B) \frac{\Delta V}{V}\propto \frac{1}{B} C) \frac{\Delta V}{V}\propto {{B}^{2}} D) \frac{\Delta v}{v}\propto {{B}^{-2}}

Answer 1

Bulk modulus is the ratio of pressure and volumetric strain .
e.g., Bulk modulus , B = pressure/volumetric strain

∵ volumetric strain = change in volume /original volume
if change in volume is ∆V
And original volume is V
Then , volumetric strian = ∆V/V

Now, B = P/∆V/V [ I didn't mention negative sign , because I just want to relation between given terms ]
∴ B $\propto$ 1/{∆V/V}
∴ ∆V/V $\propto$ 1/B

Hence, option (B) is correct.