Mechanical Properties Of Solids Question 3
Question 3 - 2024 (27 Jan Shift 1)
If average depth of an ocean is $4000 \mathrm{~m}$ and the bulk modulus of water is $2 \times 10^{9} \mathrm{Nm}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is (Given, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )
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Answer: (2)
Solution:
$\mathrm{B}=-\frac{\Delta \mathrm{P}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)}$
$-\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)=\frac{\rho \mathrm{gh}}{\mathrm{B}}=\frac{1000 \times 10 \times 4000}{2 \times 10^{9}}$
$=2 \times 10^{-2}$ [-ve sign represent compression ]
