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Chapter 7: Problem 884

In steel the young's modulus and the strain at the breaking point are $2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\( and \)0.15$ respectively the stress at the breaking point for steel is therefore........... (A) \(1.33 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(1.33 \times 10^{12}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(7.5 \times 10^{-13}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(3 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

Short Answer

Expert verified
The stress at the breaking point for steel is \(3 \times 10^{10}\mathrm{~N/m^2}\).

Step by step solution

01

Identify the given values and formula

We are given: - Young's Modulus (E) = \(2 \times 10^{11} \mathrm{~N/m^2}\) - Strain at the breaking point (ε) = 0.15 We will use the formula: σ = E ε
02

Calculate the stress at the breaking point

Plug the given values into the formula: σ = \((2 \times 10^{11})(0.15)\)
03

Solve for the stress at the breaking point

Multiplying the given values, we get: σ = \(3 \times 10^{10}\mathrm{~N/m^2}\)
04

Match the calculated stress with the given options

We look for the option that matches our calculated stress: (A) \(1.33 \times 10^{11}\mathrm{~N/m^2}\) (Incorrect) (B) \(1.33 \times 10^{12}\mathrm{~N/m^2}\) (Incorrect) (C) \(7.5 \times 10^{-13}\mathrm{~N/m^2}\) (Incorrect) **(D) \(3 \times 10^{10}\mathrm{~N/m^2}\) (Correct)** Thus, the stress at the breaking point for steel is \(3 \times 10^{10}\mathrm{~N/m^2}\), and the correct answer is (D).

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Most popular questions from this chapter

A vessel contains \(110 \mathrm{~g}\) of water the heat capacity of the vessel is equal to \(10 \mathrm{~g}\) of water. The initial temperature of water in vessel is \(10^{\circ} \mathrm{C}\) If \(220 \mathrm{~g}\) of hot water at \(70^{\circ} \mathrm{C}\) is poured in the vessel the Final temperature neglecting radiation loss will be (A) \(70^{\circ} \mathrm{C}\) (B) \(80^{\circ} \mathrm{C}\) (C) \(60^{\circ} \mathrm{C}\) (D) \(50^{\circ} \mathrm{C}\)

Cross-sectional area o if wire of length \(L\) is \(A\). Young's modulus of material is \(\mathrm{Y}\). If this wire acts as a spring what is the value of force constant? (A) (YA/L) (B) (YA/2L) (C) (2YA/L) (D) ( \(\mathrm{YL} / \mathrm{A})\)

If the young's modulus of the material is 3 times its modulus of rigidity. Then what will be its volume elasticity? (A) zero (B) infinity (C) \(2 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(3 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

The pressure applied from all directions on a cube is \(\mathrm{P}\). How much its temperature should be raised to maintain the orginal volume ? The volume elasticity, of the cube is \(\beta\) and the coefficient of volume expansion is \(\alpha\). (A) \([\mathrm{P} / \alpha \beta]\) (B) \([\mathrm{P\alpha} / \beta]\) (C) \([\beta \mathrm{p} / \alpha]\) (D) \([\alpha \beta / \mathrm{p}]\)

In a capillary tube water rises by \(1.2 \mathrm{~mm}\). The height of water that will rise in another capillary tube having half the radius of the first is (A) \(1.2 \mathrm{~mm}\) (B) \(2.4 \mathrm{~mm}\) (C) \(0.6 \mathrm{~mm}\) (D) \(0.4 \mathrm{~mm}\)
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