First slide

Elastic behaviour of solids

Question

The average depth of Indian ocean is about 3000 m. Find the percentage of compression $\frac{ΔV}{V}$ of water of the bottom of the ocean. Given, bulk modulus of water is $2 .2 \times 10^{9} {Nm}^{- 2}$ and density of water $= 1000 {kgm}^{- 3}$ .

Moderate

Solution

The increase in pressure is $Δp = ρgh$
Or $Δp = 10^{3} \times 9 .8 \times 3000 = 29 .4 \times 10^{6} {Nm}^{- 2}$
The volume strain $= \frac{ΔV}{V} = \frac{Δp}{B} = \frac{29 .4 \times 10^{6}}{2 .2 \times 10^{9}} = 1 .36 %$

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