Topic: Fluid Mechanics
A liquid compressed in cylinder has a volume of $0.04~m^{3}$ at $50~kg/cm^{2}$ and a volume of $0.039~m^{3}$ at $150~kg/cm^{2}.$ The bulk modulus of liquid is
- A. $400~kg/cm^{2}$
- B. $4000~kg/cm^{2}$
- C. $40\times10^{5}kg/cm^{2}$
- D. $40\times10^{6}kg/cm^{2}$
Answer: B. $4000~kg/cm^{2}$
Explanation: Given, $P_{1}=50~kg/cm^{2}$, $P_{2}=150~kg/cm^{2}$, $V_{1}=0.04~m^{3}$, $V_{2}=0.039m^{3}$. Bulk modulus $K=-\frac{Vdp}{dV} = -\frac{0.04(150-50)}{(0.039-0.04)} = \frac{0.04\times100}{0.001} = 4000kg/cm^{2}$.