Question

Q.3 The equation of a state for a liquid is
p = (3500 p"2 + 2500) N/m2. The bulk modulus
of liquid at a pressure of 100 kPa is
(a) 3500 N/m2 (b) 2500 N/
m2
(c) 48750 N/m2 (d) 6250 N/m2​

Answer 1

Answer:

C is correct.

refer to the attached picture for answer

Answer 2

Conclusion

The Bulk Modulus

The bulk modulus is a numerical constant that describes the elastic properties of a solid or fluid under pressure on all surfaces. When pressure is applied to a material, its volume decreases, but it returns to its original volume when the pressure is removed.

Main content

So the correct answer is C 48750 $N/m^2$

$P = (3500 S^\frac{1}{2} + 2500 )\\100000 = 3500 S^\frac{1}{2} + 2500\\S = (\frac{100000 - 2500}{3500} )^2 = 776kg/m^3\\i.e., dP = 3500 \times \frac{1}{2} S^{1-}^\frac{1}{2} dS\\\frac{dP}{dS} = 3500 \times \frac{1}{2} S^{\frac{-1}{2} } = 62.82\\i.e., K = S \frac{dP}{dS} = 48748.71 N/m^2$

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