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A ball dropped into a lake of depth 200 m shows a 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball? (Use P = rho*g*h, with rho_water = 10³ kg/m³, g = 9.8 m/s²)
- 19.6 * 10⁸ N/m²
- 19.6 * 10⁻¹⁰ N/m²
- 19.6 * 10¹⁰ N/m²
- 19.6 * 10⁻⁸ N/m²
Correct answer: 19.6 * 10⁸ N/m²
Solution
P = 1000 * 9.8 * 200 = 1.96 * 10⁶ Pa. Volumetric strain = 0.001. B = P / strain = 1.96e6 / 0.001 = 1.96 * 10⁹ = 19.6 * 10⁸ N/m².
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