Depth of a river is 100 m . Magnitude of compressibility of the water is $0.5 imes 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$. The fractional compression in water at the bottom of the river is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

Question

Depth of a river is 100 m . Magnitude of compressibility of the water is $0.5 	imes 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$. The fractional compression in water at the bottom of the river is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

Aicharya · Accepted Answer

Compressibility, $\mathrm{k}=0.5 	imes 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$ Pressure, $\mathrm{P}=\delta \mathrm{gh}=10^3 	imes 10 	imes 100=10^6 \mathrm{Nm}^{-2}$ $	herefore \mathrm{K}=\frac{1}{\mathrm{~B}}=\frac{(\Delta \mathrm{v} / \mathrm{v})}{\mathrm{P}}$ $	herefore$ Fractional change in volume, $\frac{\Delta \mathrm{V}}{\mathrm{V}}=\mathrm{KP}=0.5 	imes 10^{-9} 	imes 10^6=0.5 	imes 10^{-3}$

Depth of a river is 100 m . Magnitude of compressibility of the water is $0.5 \times 10^{-9}…

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