Question

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

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

Answer 1

The correct option is C $9.1\times {10}^{-4}{\text{m}}^3$

Bulk modulus is defined as
$K=\frac{P}{\Delta V/V}\therefore \Delta V=\frac{PV}{K}$
Here
$P=h\rho g=200\times {10}^3\times 10{\text{N/m}}^2$
$K=22000\text{atm}=22000\times {10}^5{\text{N/m}}^2$
$V=1{\text{m}}^3$

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