The fractional compression of water at the depth of 2.5 km below the sea level is _____%. Given, the Bulk modulus of water , density of water , acceleration due to gravity g = 10 . [2025]

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Solution

Q.
The fractional compression $(\frac{△ V}{V})$ of water at the depth of 2.5 km below the sea level is _____%. Given, the Bulk modulus of water = $2 \times 10^{9} {Nm}^{- 2}$ , density of water $= 10^{3} kg m^{- 3}$ , acceleration due to gravity g = 10 ${ms}^{- 2}$ . [2025]

1 1.75

2 1.0

3 1.5

4 1.25

Ans.
(4)

$B = \frac{△ P}{- (\frac{△ V}{V})}$

$\Rightarrow - (\frac{△ V}{V}) = \frac{△ P}{B} = \frac{ρ g h}{B}$

$= \frac{10^{3} \times 10 \times 2.5 \times 10^{3}}{2 \times 10^{9}} = 1.25 %$

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