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Chapter 7: Problem 975

Pressure on an object increases from \(1.01 \times 10^{\circ} \mathrm{Pa}\) to \(1.165 \times 10^{5} \mathrm{~Pa}\). He volume decrease by \(10 \%\) at constant temperature. Bulk modulus of material is........... (A) \(1.55 \times 10^{5} \mathrm{~Pa}\) (B) \(51.2 \times 10^{5} \mathrm{~Pa}\) (C) \(102.4 \times 10^{5} \mathrm{~Pa}\) (D) \(204.8 \times 10^{5} \mathrm{~Pa}\)

Short Answer

Expert verified
The bulk modulus of the material is (B) \(51.2 \times 10^{5} \mathrm{~Pa}\).

Step by step solution

01

Determine the Change in Pressure

Calculate the change in pressure ΔP by subtracting the initial pressure from the final pressure: ΔP = Final Pressure - Initial Pressure ΔP = \(1.165 \times 10^{5} \mathrm{~Pa}\) - \(1.01 \times 10^{\circ} \mathrm{Pa}\)
02

Calculate the Volumetric Strain

Given that the volume decreases by 10%, we can find the volumetric strain (ΔV/V) using the percentage decrease: Volumetric Strain = ΔV/V = - 10%
03

Calculate the Bulk Modulus

Use the Bulk modulus formula and substitute the values calculated in Step 1 and Step 2: Bulk Modulus (K) = \(- \frac{ΔP}{ΔV/V}\) K = \(- \frac{1.165 \times 10^{5} \mathrm{~Pa} - 1.01 \times 10^{\circ} \mathrm{Pa}}{-0.1}\)
04

Identify the Correct Answer

Calculate the Bulk Modulus value and see which option it matches with: K ≈ 51.2 × \(10^{5} \mathrm{~Pa}\) The correct answer is (B) \(51.2 \times 10^{5} \mathrm{~Pa}\).

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Most popular questions from this chapter

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