Question

The average depth of Indian Ocean is about $3000m$. The fractional compression, $\frac{\Delta V}{V}$ of water at the bottom of the ocean is then
(Given: Bulk modulus of the water$=2.2\times {10}^{9}N{m}^{-2}$ and $g=10m{s}^{-2}$)

• A. $0.82$%
• B. $0.91$%
• C. $1.36$%
• D. $1.24$%

Answer 1

The correct option is C $1.36$%

The pressure exerted by a $3000m$ column of water on the bottom layer is
$P=h\rho g=3000m\times 1000kg{m}^{-3}\times 10m{s}^{-2}=3\times {10}^{7}N{m}^{-2}$
Fractional compression $\frac{\Delta V}{V}$ is
$\frac{\Delta V}{V}=\frac{P}{B}=\frac{3\times {10}^{7}N{m}^{-2}}{2.2\times {10}^{9}N{m}^{-2}}=1.36\times {10}^{-2}=1.36$%