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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

A tank is filled with water up to a height \(\mathrm{H}\). Water is allowed to come out of a hole P in one of the walls at a depth \(\mathrm{D}\) below the surface of water express the horizontal distance \(\mathrm{x}\) in terms of \(\mathrm{H}\) and \(\mathrm{D}\). (B) $\left.\mathrm{x}={ }^{\alpha} \sqrt{[}\\{\mathrm{D}(\mathrm{H}-\mathrm{D})\\} / 2\right]$ (D) \(\mathrm{x}=4[\mathrm{D}(\mathrm{H}-\mathrm{D})]\)

When \(100 \mathrm{~N}\) tensile force is applied to a rod of $10^{-6} \mathrm{~m}^{2}\( cross-sectional area, its length increases by \)1 \%$ so young's modulus of material is \(\ldots \ldots \ldots \ldots\) (A) \(10^{12} \mathrm{~Pa}\) (B) \(10^{11} \mathrm{~Pa}\) (C) \(10^{10} \mathrm{~Pa}\) (D) \(10^{2} \mathrm{~Pa}\)

Assertion and Reason: Read the assertion and reason carefully to mark the correct option out of the option given below (A) If both assertion and reason are true and reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not the correct explanation of the assertion. (C) If assertion is true but reason is false. (D) If assertion and reason both are false. Assertion: The stretching of a coil is determined by its shear modulus. Reason: Shear modulus change only shape of a body keeping its dimensions unchanged. (A) a (B) \(\mathrm{b}\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

Which is the dimensional formula for modulus of rigidity? (A) \(\mathrm{M}_{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\) (B) \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\) (C) \(\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-1}\) (D) \(\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\)

The work done increasing the size of a soap film from $10 \mathrm{~cm} \times 6 \mathrm{~cm}\( to \)10 \mathrm{~cm} \times 11 \mathrm{~cm}\( is \)3 \times 10^{-4}$ Joule. The surface tension of the film is (A) \(1.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (B) \(3.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (C) \(6.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) (D) \(11.0 \times 10^{-2} \mathrm{~N} / \mathrm{m}\)
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