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 (given that the bulk modulus of the water $=2.2\times 10^{9} \, N m^{- 2 \, \, }\text{and} \, g=10 \, m s^{- 2}$ ) is

• A. 0.82%
• B. 0.91%
• C. 1.36%
• D. 1.52%

Answer 1

Answer: (C)

The bulk modulus of elasticity is given by
$B=\frac{P}{\frac{\Delta V}{V}}$
So, fractional compression $\frac{\Delta V}{V}=\frac{P}{B}$
The pressure at the depth $h$ in fluid is given as $P=h\rho g$
$\frac{\Delta V}{V}=\frac{\rho g h}{B}\Rightarrow \frac{\Delta V}{V}\times 100=\frac{1000 \times 10 \times 3000}{2 . 2 \times 10^{9}}\times 100=1.36\%$