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Question: The average depth of Indian ocean is about 3000 m. The fractional compression, \(\frac{\Delta V}{V}\...

The average depth of Indian ocean is about 3000 m. The fractional compression, ΔVV\frac{\Delta V}{V}of water at the bottom of the ocean is (Given : Bulk modulus of the water =2.2×109 N m−2 and g= m s−2= 2.2 \times 10^{9}\text{ N }\text{m}^{- 2}\text{ and }g = \text{ m }\text{s}^{- 2}

A

0.82%

B

0.91%

C

1.36%

D

1.24%

Answer

1.36%

Explanation

Solution

: The pressure exerted by a 3000 m column of water on the bottom layer is

P=hρgP = h\rho g

=3000m×1000kgm−3×10ms−2= 3000m \times 1000kgm^{- 3} \times 10ms^{- 2}

=3×107Nm−2= 3 \times 10^{7}Nm^{- 2}

Fractional compressionΔVVis\frac{\Delta V}{V}is

ΔVV=PB=3×107Nm−2Nm−22.2×109Nm−2\frac{\Delta V}{V} = \frac{P}{B} = \frac{3 \times 10^{7}Nm^{- 2}Nm^{- 2}}{2.2 \times 10^{9}Nm^{- 2}}=1.36×10−2=1.36%1.36 \times 10^{- 2} = 1.36\%