If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10 9 N m - 2 , then fractional compression Δ V V of water at the bottom of ocean is α × 10 - 2 . The value of α is _______,

Question

If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10 9 N m - 2 , then fractional compression Δ V V of water at the bottom of ocean is α × 10 - 2 . The value of α is _______, (Given, g = 10 m s - 2 , ρ = 1000 kg m - 3 )

TestHub · Accepted Answer

The formula to calculate the Bulk modulus is given by

$B = - \frac{∆ P}{(\frac{∆ V}{V})} . . . (1)$

From equation (1), the fractional compression in volume may be obtained as follows:

$\begin{array}{rcl} - (\frac{Δ V}{V}) & = & \frac{∆ P}{B} \\ = & \frac{ρ g ∆ h}{B} . . . (2) \end{array}$

From equation (2) it follows that

$\begin{array}{rcl} |- (\frac{∆ V}{V})| & = & \frac{1000 \times 10 \times 4000}{2 \times 10^{9}} \\ \Rightarrow & (\frac{∆ V}{V}) = 2 \times 10^{- 2} \end{array}$

Hence, $α = 2$ .

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