Aluminium sphere: fractional volume change under pressure

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Question

A solid aluminium sphere is subjected to a hydraulic pressure of 1 × 107 N/m2. If the bulk modulus of aluminium is 7.2 × 1010 N/m2, what is the fractional change in volume?

Choose one · Correct answer highlighted

1.39 × 10-4 Correct 2 × 10-4 1 × 10-4 3 × 10-4

Bulk modulus: B = -p / (ΔV / V). Rearrange: ΔV / V = -p / B. Substitute: ΔV / V = -(1 × 107) / (7.2 × 1010) ≈ -1.39 × 10-4. Magnitude: 1.39 × 10-4.

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