Question 244: Properties of Matter

Question

If average depth of an ocean is $$4000 \mathrm{~m}$$ and the bulk modulus of water is $$2 	imes 10^9 \mathrm{~Nm}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha 	imes 10^{-2}$$. The value of $$\alpha$$ is _______ (Given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, ho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$)

Accepted Answer

$$\begin{aligned}
& \mathrm{B}=-\frac{\Delta \mathrm{P}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}ight)} \
& -\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}ight)=\frac{ho \mathrm{gh}}{\mathrm{B}}=\frac{1000 	imes 10 	imes 4000}{2 	imes 10^9} \
& =2 	imes 10^{-2}[-\mathrm{ve} 	ext { sign represent compression }]
\end{aligned}$$

Properties of Matter

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