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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

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) \(10^{2} \mathrm{~Pa}\)

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the 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 the assertion and reason both are false. Assertion: Tiny drops of liquid resist deforming forces better than bigger drops. Reason: Excess pressure inside a drop is directly proportional to surface tension. (A) a (B) \(b\) (C) (D) d

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) ( \(\mathrm{YL} / \mathrm{A})\)

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) \(204.8 \times 10^{5} \mathrm{~Pa}\)

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 the reason is the correct explanation of the reason. (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 the assertion and reason both are false. (e) If assertion is false but reason is true. Assertion: The molecules of \(0^{\circ} \mathrm{C}\) ice and $0^{\circ} \mathrm{C}$ water will have same potential energy. Reason: Potential energy depends only on temperature of the system. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) d (E) e
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