Question

The average depth of Indian ocean is about $3000m$ . The value of fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at the bottom of the ocean is (given that the bulk modulus of water is $2.2\times 10^{9}N{m}^{-2}$ , $g=9.8$ , ${\rho }_{H_{2}O}=1000kg.m^{-3}$ )

• A. $3.4\times 10^{-2}$
• B. $1.34\times 10^{-2}$
• C. $4.13\times 10^{-2}$
• D. $13.4\times 10^{-2}$

Answer 1

Answer: (B)

The fractional compression or decrease in volume
$\frac{\Delta V}{V}=\frac{h\rho g}{k}$
where, $h=$ depth (average)
$\rho =$ density of ocean water
$g=$ gravitational acceleration and
$k=$ bulk modulus
$\Rightarrow \frac{\Delta V}{V}=\frac{3\times 10^3\times 10^3\times 9.8}{2.2\times 10^9}$
$=\frac{3}{2.2}\times 10^{-4}\times 98$
$=\frac{147}{11}\times 10^{-4}=1.34\times 10^{-2}$