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A ball sinking in a lake of depth 200 m undergoes a 0.1% reduction in volume at the bottom. Find the bulk modulus of the ball's material. (Use P = rho g h, rho = 1000 kg/m³, g = 9.8 m/s²)

1. 19.6 * 10⁸ N/m²
2. 19.6 * 10⁻¹⁰ N/m²
3. 19.6 * 10¹⁰ N/m²
4. 19.6 * 10⁻⁸ N/m²

Correct answer: 19.6 * 10⁸ N/m²

Solution

The pressure at 200 m is 1.96*10⁶ Pa and the fractional volume change is 0.001, so B = P/(dV/V) = 1.96*10⁹ Pa = 19.6*10⁸ N/m².

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