Question

$1m^3$ water is brought inside the lake upto $200m$ depth from the surface of the lake. What will be change in the volume when the bulk modulus of elasticity of water is $22000atm$?
(density of water is $1\times {10}^{3}kg/m^3$ atmosphere pressure = ${10}^{5}N/m^2$ and $g=10m/s^2$

• A. $8.9\times {10}^{-3}{m}^3$
• B. $7.8\times {10}^{-3}{m}^3$
• C. $9.1\times {10}^{-4}{m}^3$
• D. $8.7\times {10}^{-4}{m}^3$

Answer 1

Answer: (C)

$9.1\times {10}^{-4}{m}^3$

$K=\frac{P}{\Delta V/V}$

$\therefore \Delta V=\frac{PV}{K}$

$P=h\rho g=200\times {10}^3\times 10N/m^2$

$K=22000atm=22000\times {10}^{5}N/m^2$

V = 1$m^3$

$\Delta V=\frac{200\times {10}^3\times 10\times 1}{22000\times {10}^5}=9.1\times {10}^{-4}{m}^3$