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Chapter 7: Problem 856

When the length of a wire having cross section area \(10^{-6} \mathrm{~m}^{2}\) is streatched by \(0.1 \%\) then tension in it is \(100 \mathrm{~N}\). Young's modulus of material wire is \(\ldots \ldots \ldots\) (A) \(10^{12}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(10^{2}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

Short Answer

Expert verified
The Young's modulus of the material of the wire is \(10^{11} (\mathrm{N} / \mathrm{m}^{2})\).

Step by step solution

01

Calculate the stress

First, we need to find the stress in the wire. Stress is defined as the force per unit area, so we can calculate it using the formula: \[stress = \frac{force}{area}\]. The force applied to the wire is the tension (100 N), and the cross-sectional area of the wire is \(10^{-6} m^2\). To calculate the stress: \[stress = \frac{100 N}{10^{-6} m^2} = 10^8\ (\mathrm{N} / \mathrm{m}^{2})\].
02

Calculate the strain

Next, we need to find the strain in the wire. Strain is the ratio of the change in length (the stretch) to the original length. We are given that the wire has been stretched by 0.1%. Since strain is unitless, we can write the strain as the decimal equivalent: \[strain = \frac{0.1}{100} = 0.001\].
03

Find Young's modulus

Now that we have calculated the stress and strain, we can use the formula for Young's modulus: \[Y = \frac{stress}{strain}\]. Plugging in the values we found in steps 1 and 2: \[Y = \frac{10^8\ (\mathrm{N} / \mathrm{m}^{2})}{0.001} = 10^{11}\ (\mathrm{N} / \mathrm{m}^{2})\]. So, the Young's modulus of the material of the wire is \(10^{11} (\mathrm{N} / \mathrm{m}^{2})\), which corresponds to option (D).

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Most popular questions from this chapter

A soap bubble of radius \(r\) is blown up to form a bubble of radius $2 \mathrm{r}\( under isothermal conditions if the \)\mathrm{T}$ is the surface tension of soap solution the energy spent in the slowing is. (A) \(3 \pi \mathrm{Tr}^{2}\) (B) \(6 \pi \mathrm{Tr}^{2}\) (C) \(12 \pi \mathrm{Tr}^{2}\) (D) \(24 \pi \mathrm{Tr}^{2}\)

Mercury thermometers can be used to measure temperatures up to (A) \(100^{\circ} \mathrm{C}\) (B) \(212^{\circ} \mathrm{C}\) (C) \(360^{\circ} \mathrm{C}\) (D) \(500^{\circ} \mathrm{C}\)

Oxygen boils at \(183^{\circ} \mathrm{C}\). This temperature is approximately. (A) \(215^{\circ} \mathrm{F}\) (B) \(-297^{\circ} \mathrm{F}\) (C) \(329^{\circ} \mathrm{F}\) (D) \(361^{\circ} \mathrm{F}\)

The amount of work done in blowing a soap bubble such that its diameter increases from \(d\) to \(D\) is \((T=\) Surface tension of solution) (A) \(4 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}\) (B) \(8 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}\) (C) \(\pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}\) (D) \(2 \pi\left(\mathrm{D}^{2}-\mathrm{d}^{2}\right) \mathrm{T}\)

The upper end of a wire of radius \(4 \mathrm{~mm}\) and length $100 \mathrm{~cm}$ is clamped and its other end is twisted through an angle of \(30^{\circ}\). Then what is the angle of shear? (A) \(12^{\circ}\) (B) \(0.12^{\circ}\) (C) \(1.2^{\circ}\) (D) \(0.012^{\circ}\)
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