An increase in pressure of 6.3×10⁷ N·m⁻² is required to produce a small decrease in the volume of water. The bulk modulus of water is 2.1×10⁹ N·m⁻². What is the percentage decrease in volume?
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Question

An increase in pressure of 6.3×10⁷ N·m⁻² is required to produce a small decrease in the volume of water. The bulk modulus of water is 2.1×10⁹ N·m⁻². What is the percentage decrease in volume?

Options

G1 Physics · Accepted Answer

Bulk modulus is defined as B = -ΔP ÷ (ΔV ÷ V). Therefore the magnitude of the fractional change in volume is |ΔV| ÷ V = ΔP ÷ B. Substitute: |ΔV| ÷ V = 6.3×10⁷ ÷ 2.1×10⁹ = 0.03. Hence the percentage decrease in volume is 0.03×100 = 3%. Correct option: B.