Mechanical Properties of Solids

JEE Main level, single correct, medium

87 of 118

Question 87 of 118

The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is
______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).

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Answer: (A) 1.25

B=ρgh(Δvv)Δvv×100=ρghB×1001000×10×2.5×1032×109×100%=1.25%\begin{aligned} & \mathrm{B}=\frac{\rho \mathrm{gh}}{\left(\frac{\Delta \mathrm{v}}{\mathrm{v}}\right)} \\ & \frac{\Delta \mathrm{v}}{\mathrm{v}} \times 100=\frac{\rho \mathrm{gh}}{\mathrm{B}} \times 100 \\ & \frac{1000 \times 10 \times 2.5 \times 10^3}{2 \times 10^9} \times 100 \% \\ & =1.25 \%\end{aligned}

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