### Related Formula B = -fracDelta Pleft(fracDelta VVright) implies left|fracDelta VVright| = fracDelta PB$B = -\frac{\Delta P}{\left(\frac{\Delta V}{V}\right)} \implies \left|\frac{\Delta V}{V}\right| = \frac{\Delta P}{B}$ Where the hydrostatic pressure difference at depth is Delta P = rho g h$\Delta P = \rho g h$. ### Core Logic Calculate the gauge pressure Delta P$\Delta P$ at the ocean floor (h = 4000text m$h = 4000\text{ m}$): Delta P = 1000 times 10 times 4000 = 4 times 10^7text N/m^2$\Delta P = 1000 \times 10 \times 4000 = 4 \times 10^7\text{ N/m}^2$ ### Step 1: Compute fractional volume change left|fracDelta VVright| = frac4 times 10^72 times 10^9 = 2 times 10^-2$\left|\frac{\Delta V}{V}\right| = \frac{4 \times 10^7}{2 \times 10^9} = 2 \times 10^{-2}$ ### Step 2: Match parameters to find alpha Comparing 2 times 10^-2$2 \times 10^{-2}$ to alpha times 10^-2$\alpha \times 10^{-2}$ gives: alpha = 2$\alpha = 2$ ### Pattern Recognition Hydrostatic scaling expressions yield precise decade cancellations when tracked directly relative to high exponent elastic constants like Bulk Moduli. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Mechanical Properties of Solids / Fluids